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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 8 — Apr. 11, 2011
  • pp: 7312–7324
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Phase locking of a 275W high power all-fiber amplifier seeded by two categories of multi-tone lasers

Xiaolin Wang, Jingyong Leng, Pu Zhou, Wenbo Du, Hu Xiao, Yanxing Ma, Xiaolin Dong, Xiaojun Xu, Zejin Liu, and Yijun Zhao  »View Author Affiliations


Optics Express, Vol. 19, Issue 8, pp. 7312-7324 (2011)
http://dx.doi.org/10.1364/OE.19.007312


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Abstract

Multi-tone radiation is a promising technique to suppress stimulated Brillouin scattering (SBS) effects and improve the ultimate output power of the fiber laser/amplifier. Coherent beam combining of fiber lasers/ amplifiers is another feasible way to increase the output laser power from single gain medium while simultaneously maintaining good beam quality. In this paper, we combine the multi-tone driven all-fiber amplifiers and active phase compensation to demonstrate high power phase locking for coherent beam combining. First, we present the theory of coherent beam combining of multi-tone lasers. Second, we optimize the all-fiber power amplifier oscillator power-amplifier (MOPA) system with high scalability and flexibility based on compact, high efficiency Yb-doped fiber amplifier chains. Then, two categories of multi-tone master oscillators are used to driven the amplifier chains. The first category is two coupled single-frequency lasers and the second is a frequency modulated single-frequency laser. The output powers are all boosted to 275W without any distinct SBS. Last, phase locking of the amplifier chains are implemented using stochastic parallel gradient descent (SPGD) algorithm. Scaling this configuration to a higher power involves increasing the power per chain and adding the number of amplifier channels.

© 2011 OSA

1. Introduction

High power single-frequency/narrow linewidth fiber lasers are widely used in materials processing, gravitational wave sensors, nonlinear frequency conversion and remote sensing [1

1. S. Gray, A. Liu, D. T. Walton, J. Wang, M. J. Li, X. Chen, A. B. Ruffin, J. A. DeMeritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17044–17050 (2007). [CrossRef] [PubMed]

, 2

2. M. D. Mermelstein, K. Brar, M. J. Andrejco, A. D. Yablon, M. Fishteyn, C. Headley III, and D. J. DiGiovanni, “All-fiber 194 W single-frequency single-mode Yb-doped master-oscillator power-amplifier,” Fiber Lasers V: Technology, Systems, and Applications, Jes Broeng and Clifford Headley eds. Proc. SPIE 6873, 68730L-1–68731L-6 (2008).

]. Nevertheless, restricted in terms of thermal load, fiber damage and nonlinear effect, the ultimate output power of the single-frequency amplifier is hundreds watt level [1

1. S. Gray, A. Liu, D. T. Walton, J. Wang, M. J. Li, X. Chen, A. B. Ruffin, J. A. DeMeritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17044–17050 (2007). [CrossRef] [PubMed]

, 3

3. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]

, 4

4. G. D. Goodno, L. D. Book, and J. E. Rothenberg, “Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier,” Opt. Lett. 34(8), 1204–1206 (2009). [CrossRef] [PubMed]

]. Up to now, stimulated Brillouin scattering (SBS) remains a major obstacle toward high-power narrow-linewidth fiber amplifiers [5

5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]

]. In order to increase to output power, two ways are suggested, one is mitigate or suppress SBS in fibers [6

6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]

10

10. I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010). [CrossRef] [PubMed]

], and the other is coherent beam combining [11

11. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammo, H. Injeyan, H. Komine, W. H. Long, M. Jr McClellan, S. J. McNau, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). [CrossRef]

15

15. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009). [CrossRef]

].

In order to mitigate SBS and increase the output power of a single fiber amplifier, a lot of techniques including large-mode area (LMA) fibers [16

16. J. P. Koplow, D. A. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25(7), 442–444 (2000). [CrossRef]

], stress [17

17. A. Wada, T. Nozawa, D. Tanaka, and R. Yamauchi, “Suppression of SBS by intentionally induced periodic residual-strain in single-mode optical fibers,” Proc. 17 th ECOC PaperB1.1, 25–28 (1991).

], thermal gradients [8

8. A. Liu, “Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient,” Opt. Express 15(3), 977–984 (2007). [CrossRef] [PubMed]

] and multi-tone driven [5

5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]

, 6

6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]

, 9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

, 10

10. I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010). [CrossRef] [PubMed]

] have been proposed and investigated. In all of these techniques, the recently suggested multi-tone driven technique may be one of the most attractive techniques for which is easy to implementation and conjunction with other techniques. It was shown that in two-tone driven amplifier, with optimal input power ratio would triple the total power output of the amplifier while preserving the power ratio without any SBS [9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. And recently, the output of a

ll-fiber single-frequency laser is boost to 230W by using gain competition technique of two-tone driven amplifier [18

18. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011). [CrossRef] [PubMed]

].

Coherent beam combining (CBC) of fiber lasers/amplifiers is another feasible way to increase the output laser power from single gain medium while simultaneously maintaining good beam quality. There are two main configurations of coherent combining, including passive phasing [12

12. L. Jianfeng, D. Kailiang, W. Yishan, Z. Wei, Z. Jianhua, and G. Yongkang, “High-power coherent beam combining of two photonic crystal fiber lasers,” IEEE Photon. Technol. Lett. 20(11), 888–890 (2008). [CrossRef]

, 19

19. L. Li, A. Schülzgen, H. Li, V. L. Temyanko, J. V. Moloney, and N. Peyghambarian, “Phase-locked multicore all-fiber lasers: modeling and experimental investigation,” J. Opt. Soc. Am. B 24(8), 1721–1728 (2007). [CrossRef]

] and active phasing configuration [20

20. J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Fiber Lasers III: Technology, Systems, and Applications, Andrew J. W. Brown, Johan Nilsson, Donald J. Harter, Andreas Tünnermann, eds., Proc. SPIE 6102, 61020U-1–61021U-5 (2006).

22

22. L. Liu, M. A. Vorontsov, E. P. Polnau, T. Weyrauch, and L. A. Beresnev, “Adaptive phase-locked fiber array with wavefront phase tip-tilt compensation using piezoelectric fiber positioners,” Atmospheric Optics: Models, Measurements, and Target-in-the-Loop Propagation, Stephen M. Hammel, Alexander M. J. van Eijk, Michael T. Valley, Mikhail A. Vorontsov, eds., Proc. SPIE 6708, 67080K-1–67081K-12 (2007).

]. Master-oscillator power-amplifier (MOPA) with active phasing configuration is one of the most effective ways for coherent combining [20

20. J. Anderegg, S. Brosnan, E. Cheung, P. Epp, D. Hammons, H. Komine, M. Weber, and M. Wickham, “Coherently coupled high power fiber arrays,” Fiber Lasers III: Technology, Systems, and Applications, Andrew J. W. Brown, Johan Nilsson, Donald J. Harter, Andreas Tünnermann, eds., Proc. SPIE 6102, 61020U-1–61021U-5 (2006).

, 21

21. T. M. Shay, V. Benham, J. T. Bake, A. D. Sanchez, D. Pilkington, and A. C. A. Lu, “Self synchronous and self-referenced coherent beam combination for large optical arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 480–486 (2007). [CrossRef]

] and the highest power demonstration of coherent combining have involved active phasing in MOPA configuration [23

23. J. M. Stuart, P. A. Charles, I. Hagop, J. Andrew, M. J. Adam, C. J. Gina, K. Hiroshi, M. Jason, M. Jay, M. Michael, S. Randy, S. Jeff, M. V. Marcy, W. Mark, and B. S. Weiss, “100-kW coherently combined Nd:YAG MOPA laser array,” in Frontiers in Optics(Optical Society of America), p. D2(2009).

]. So far, there are four main techniques are reported for active phase control, digital holography technique [24

24. C. Bellanger, M. Paurisse, A. Brignon, J. Colineau, J. P. Huignard, M. Hanna, F. Druon, and P. Georges, “Coherent fiber combining by digital holography,” in Lasers and Electro-Optics (CLEO) and Quantum Electronics and Laser Science Conference (QELS), pp. 1–2(2010).

], heterodyne phase detection technique [11

11. G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammo, H. Injeyan, H. Komine, W. H. Long, M. Jr McClellan, S. J. McNau, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). [CrossRef]

, 25

25. S. J. Augst, T. Y. Fan, and A. Sanchez, “Coherent beam combining and phase noise measurements of ytterbium fiber amplifiers,” Opt. Lett. 29(5), 474–476 (2004). [CrossRef] [PubMed]

], multi-dither technique [13

13. V. Jolivet, P. Bourdon, B. Bennai, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouen, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009). [CrossRef]

, 26

26. T. M. Shay, V. Benham, J. T. Baker, B. Ward, A. D. Sanchez, M. A. Culpepper, D. Pilkington, J. Spring, D. J. Nelson, and C. A. Lu, “First experimental demonstration of self-synchronous phase locking of an optical array,” Opt. Express 14(25), 12015–12021 (2006). [CrossRef] [PubMed]

], and stochastic parallel gradient descent (SPGD) algorithm technique [14

14. M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15(2), 269–280 (2009). [CrossRef]

, 15

15. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009). [CrossRef]

]. For the advantage of mode-free, simple to implement, and easy to construct a compact system, SPGD algorithm may be the most prospective techniques and has been proposed for building new architecture of high energy laser system Adaptive Photonics Phase-Locked Elements (APPLE) [27

27. M. Vorontsov, “Adaptive photonics phase-locked elements (APPLE): system architecture and wavefront control concept,” Target-in-the-Loop: Atmospheric Tracking, Imaging, and Compensation II, Michael T. Valley, Mikhail A. Vorontsov, eds., Proc. SPIE 5895, 589501-1–589501-9 (2005).

]. But so far, high power demonstration for coherent beam combining of multi-tone amplifiers using SPGD algorithm had not been demonstrated yet.

In this paper, we combine the multi-tone driven all-fiber amplifier and active phase compensation to demonstrate high power coherent beam combining. We will first present the demonstration of 275W output all-fiber amplifier seeded by two categories of multi-tone lasers, which we believe to be the highest power in multi-tone driven amplifiers with all-fiber configuration. Here, the first category multi-tone laser is two coupled single-frequency lasers and the second is a frequency modulated single-frequency laser. Then, we will present the demonstration of the phase locking of the amplifier chain using SPGD algorithm, which is consider to be the first step for coherent beam combining of multi-tone driven amplifiers.

2. Theory of SBS mitigation in multi-tone driven amplifiers and theory for coherent beam combining of multi-tone single-frequency lasers

2.1 SBS mitigation in two-tone driven all-fiber amplifier

In single-tone driven amplifier, SBS is the most important nonlinear effect, and the phonon field can be mathematically decoupled from the photon fields leading to a 2×2 coupled nonlinear system of differential equations for the signal and Stokes light [5

5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]

]. While in two-tone driven amplifier, 7 optical fields (including 2 signals, 2 Stokes lights, 2 four-wave mixing (FWM) sidebands and 1 pump signal) are coupled with each other through the population density and the signal/Stokes gains [9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. This will result in power transfer from the Stokes waves into the signal lasers [6

6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]

, 9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. Therefore, two-tone driven amplifier can increase the SBS threshold and improve the output power [9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. For multi-tone driven amplifiers with more than two tones, the coupled nonlinear differential equations will be similar but more complex, and SBS will be suppressed more efficiently [5

5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]

].Experiment results show that strong FWM will appear if the wavelength separation between each signal is twice of the Brillouin-shift of the signals [6

6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]

], while large wavelength separation can mitigate the FWM and even lead to a single-frequency laser output through gain competition [18

18. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011). [CrossRef] [PubMed]

]. In this paper, we will demonstrate that multi-tone technique with two types of multi-tone lasers. The first one is two laser coupled with wavelength separation lager than twice of Brillouin-shift but smaller than that value (20nm) in reference [18

18. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011). [CrossRef] [PubMed]

]. The other one is a frequency modulated single-frequency laser with linewidth separation of about 100MHz.

2.2 Coherent beam combining of multi-tone single-frequency laser

It was previously thought that single-frequency seed laser is necessary to improve the spatial coherence property and obtain high brightness interference pattern in coherent beam combining [28

28. J. Limpert, F. Röser, S. Klingebiel, T. Schreiber, C. Wirth, T. Peschel, R. Eberhardt, and A. Tünnermann, “The rising power of fiber lasers and amplifiers,” IEEE J. Sel. Top. Quantum Electron. 13(3), 537–545 (2007). [CrossRef]

]. Otherwise, precise optical path difference control is needed to ensure the coherence property [29

29. G. D. Goodno, S. J. McNaught, J. E. Rothenberg, T. S. McComb, P. A. Thielen, M. G. Wickham, and M. E. Weber, “Active phase and polarization locking of a 1.4 kW fiber amplifier,” Opt. Lett. 35(10), 1542–1544 (2010). [CrossRef] [PubMed]

]. Here we will present that coherent beam combining using multi-tone single-frequency lasers is another alternative way for power scaling up.

Consider coherent beam combining of M channel N-tone (which means each channel has N single-frequency laser) lasers, the electric field of the mth channel laser in frequency νn is
Em,n(t)=Em,nej2πνnt,
(1)
Where Enis the amplitude andνn is the frequency of the laser, νnis given byνn=ν0+[n(N+1)/2]Δν andm=1,2,...,M,n=1,2,...,N.

The combined intensity is the none-coherent addition of every coherent combined single-frequency laser

I=n=1NIνn(rm,t)=n=1N|Eνn(rm,t)|2,
(2)

HereEνn(rm,t) is given by
Eνn(rm,t)=m=1MEm,nej(2πνntκnrm),
(3)
where κn=2πνnc, rmis the optical path of the mth channel. Then, combined intensity is given by

I=n=1NIνn(rm,t)=n=1Nmi=1Mmj=1MEmi,nEmj,nej2πvnc(rmirmj),
(4)

LetEm,n=1, the combined intensity can be reduced to

I=mi=1Mmj=1Mej2π(v0(N1)Δν/2)c(rmirmj)1ej2πNΔνc(rmirmj)1ej2πΔνc(rmirmj),
(5)

If there are only two channels for coherent beam combining, evolution of the intensity versus optical path difference Δl is

I=2(N+sin(NπdvΔlc)sin(πdvΔlc)cos(2πν0Δlc)),
(6)

The visibility (define asV=(ImaxImin)/(Imax+Imin)) of the interference pattern is

V=|sin(NπdvΔlc)Nsin(πdvΔlc)|,
(7)

Here, the visibility is a periodical function of the optical path difference with a period of LT = c/. When the optical path difference is dL=kLT, the visibility gets its maximum values, when the optical path difference is dL=(k+1/2)LT, the visibility gets its minimum values. Where k = 0, 1, 2,….

In our experiment, two categories of multi-tone seeds are used for power amplify. The first one is two coupled single-frequency lasers and the second is a frequency modulated single-frequency laser. We will investigate the characteristic of coherent beam combining of two seeds by simulations briefly.

2.2.1 Coherent beam combing of two-tone single-frequency laser

Consider two channel coherent beam combining of two single-frequency lasers in our experiment, the wavelengths are 1063.8nm and 1064.4nm, respectively. When the Eq. (4), we calculate the intensities and visibilities in difference power ratio, shown in Fig. 1
Fig. 1 Evolution of intensities and visibilities versus optical path difference in difference power ratio. (a) P1:P2=0.5:0.5, (b) P1:P2=0.66:0.33, (c) P1:P2=0.8:0.2.
. Figure 1(a), 1(b), 1(c) are the results for power ratio of P1:P2=0.5:0.5, P1:P2=0.66:0.33, and P1:P2=0.8:0.2 respectively. Results show that the intensities and the visibilities are modulated with an optical path difference period of LT=0.0019m (LT=c/). The visibilities gets the maximum value when the optical path difference (dL) is 19k mm, and gets the minimum value when dL is 9.5(k+1/2) mm. As the power ratio increases, the mean value and the minimal value of the visibilities both increase. In Fig. 1, the mean visibilities are 0.63, 0.71and 0.81, and the minimum visibilities are 0, 0.33, and 0.59, respectively. The visibilities can reach 0 only when the power ratio is 0.5:0.5.

2.2.2 Coherent beam combing of frequency modulated single-frequency laser

The frequency modulated single-frequency laser is a multi-tone seed and can be used for SBS suppression and power scaling in multi-tone driven amplifiers. Detail analyses are shown as follows.

The electric field of the single-frequency laser is

E(t)=E0ejω0t,
(8)

When modulated by a sine wave signal
φ(t)=ψ0cos(ωmt+ϕ0),
(9)
whereψ0, ωm and ϕ0are the amplitude, frequency and initial phase of the modulation signal respectively.

The output electric field is given by

Emd(t)=E0ej(ω0t+ψ0cos(ωmt+ϕ0)),
(10)

Using the Bessel function, Equ.10 can be written as

Emd(t)=n=jnJn(ψ0)ejnϕ0ej(ω0+nωm)t,
(11)

Here Jn(ψ0)is the first kind of Bessel function. As the result of the sine wave phase modulation, multi-tone laser with infinite sideband is generated. The frequency of each sideband isω0+nωmand corresponding amplitude isJn(ψ0).

With Eq. (11), we compute intensity of the sidebands from −25 to 25 orders when a 1064.4nm laser is modulated by a 100MHz sine wave signal with modulation amplitude of π/2. Results are both shown in linearity and dB scale (Fig. 2(a)
Fig. 2 (a) Intensity distribution of frequency modulated laser and (b) evolution of intensity and visibility versus optical path difference
). Figure 2 (b) shows the evolution of intensity and visibility versus optical path difference in two channel coherent beam combining of the frequency-modulated laser. The visibility is a function of optical path difference with a period of LT =3m (LT =c/=3). The visibility gets the maximum value when dL=kLT, and gets the minimum value when dL=LT (k±1/3), k=0,1,2,… .

It is predicated that the visibilities in coherent beam combining of two categories of multi-tone lasers are function of optical path difference dL. In experiment, high visibility interference pattern can be obtained when the optical path difference is dL=kLT, accurately control the optical path difference to be zero is not necessary.

3. Experimental demonstration and phase locking of two categories multi-tone driven high power amplifier with all-fiber configuration

3.1 Two categories multi-tone driven high power amplifiers with all-fiber configuration

3.1.1 Experimental setup of multi-tone driven amplifiers

The experimental setup is shown in Fig. 3
Fig. 3 Experimental setup of the multi-tone driven amplifier. (a) Configuration of master oscillator, preamplifier and splitters. (b) Configuration of three stage power amplifier. MO: master oscillator, CI.1, C1, C2: coupler. ISO: isolator, WDM: wavelength division multiplexer. YDF: Yb3+ doped fiber, PM: phase modulator. PD1, PD2, PD3, PDI.1, PDI.2, PDI.3, PDII.1, and PDII.2: photodetector, SMFC: single-mode filter coupler.
, two categories multi-tone seeds are used as the master oscillator (MO). The first MO is two coupled single-frequency lasers. Seed 1 is a commercial single-frequency laser (RLFM-25-1-1064-1, NP Photonics inc.) with center wavelength 1064.4nm, linewidth ~87 kHz. Seed 2 is a single-frequency laser provided by South China University of Technology, with center wavelength 1063.8nm, linewidth ~250 kHz. In this type of multi-tone MO, as the wavelength separation is much lager than twice of the Brillouin-shift [6

6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]

], not only the SBS will be suppressed, but also the FWM effect can be mitigated [9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. Compared with the signals used in reference [18

18. C. Zeringue, C. Vergien, and I. Dajani, “Pump-limited, 203 W, single-frequency monolithic fiber amplifier based on laser gain competition,” Opt. Lett. 36(5), 618–620 (2011). [CrossRef] [PubMed]

], as the separation between the two single-frequency signals is much smaller, there are no effective gain competition and both two of the signals will be amplified. Moreover, in reference [10

10. I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010). [CrossRef] [PubMed]

], on of the signal is broadband laser, which provide the ability for SBS suppression itself. But in our experiment, two lasers are single-frequency laser, SBS suppression is realized by the coupling of different optical fields in the amplifiers [9

9. I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

]. The second MO is a frequency modulated single-frequency laser. In experiment, seed1 is frequency modulated by a high speed phase modulator (PM, NIR-MPX-LN-10-P-P-FA-FA, Photoline inc., half voltage ~9V, insert loss ~3.0dB) and multi-tone laser with infinite sideband is generated. The MO is first scaled up to 300mW by a preamplifier (A0), and then split into 9 channels by a 1X9 splitter. Each channel coupled into a phase modulator (PM, NIR-MPX-LN-0.1-P-P-FA-FA, Photoline inc., half voltage 2.2V, insert loss 3.0dB), and then send to a three stage power amplifier chain. Although the laser power from master oscillator is split into nine channels, in our present experiment two of them are employed.

The configuration of three stage power amplifier chain is all-fiber based, as shown in Fig. 3(b). Three stage power amplifier chain scales the power from 15mW more than 300W (15mW to 150mW in AI.1, 150mW to 9W in AII.1, 9W to more than 300W in AIII.1), depending on the pumps. After the output of the first two stage amplifiers, single-mode filter couplers (SMFC, with which a signal power ratio 0.1% is coupled to the tap) and photodetectors (PD) are used to monitor the output and the backward lasers. In AII.1, PDII.1 is used to monitor the SBS which may generate in the main power amplifier (AIII.1). Monitor circuit is designed to detect the power in the PII.1 and to control the power supply of pumps in AIII.1. When the power detected by PDII.1 is more than 0.15mW (which mean the total power of the backward power in the SMFC is ~150mW), the power supply of the pumps in main amplifier is turnoff by the control circuit, which can avoid the damage caused by the SBS and protect the amplifier chains. In order to avoid turn off the power supply unpredictably, we carefully tune the power supply to ensure the backward power is less than 100mW. Therefore, when the backward power in the SMFC is 100mW, corresponding power of the main amplifier is consider to the ultimate one.

Main power amplifier is based on a ~3.5 m long large-mode area (LMA) SM ytterbium-doped fiber (YDF) for high power operation (LMA-YDF-30/250, Nufern inc.). The LMA fiber has a 30 μm diameter core with NA 0.08, and the inner cladding diameter is 250 μm with NA 0.46. The LMA is pump by six 60W level 974 nm laser diodes through a (6+1)X1 combiner (with 15/130μm output fiber, ITF inc.). A 0.5 m long double-clad passive fiber of the same core/inner cladding diameter and NA with the LMA YDF is spliced to the LMA YDF for power delivery. The spliced region is covered in high-index gel to strip the residual pump laser and high order mode laser in the inner cladding of the fiber. The output end of the delivery fiber is 8° angle cleaved to suppress spurious lasing as a result of Fresnel reflections.

3.1.2 Experimental results of multi-tone driven amplifiers

We first investigate the power characteristic of the single-tone driven amplifier chain. When the power coupled into the main amplifier is ~5W, output power characteristic is shown in Fig. 4
Fig. 4 Output and backward power characteristic of the amplifier chains seeded by (a) seed 1 and (b) seed2
. The ultimate powers (when the backward power in the SMFC is about 100mW) of the amplifier are 120 W (Fig. 4(a)) and 168W (Fig. 4(b)) when driven by seed 1 and seed 2, respectively. The power conversion efficiencies are about 64.86% and 74.57%, respectively. It is shown that seed 2 provide higher power conversion efficiency than seed 1. The main reason is that the frequently shifted center wavelength (as there are no temperature and cavity length control measures, the tested center wavelength of seed laser 2 shifts frequently) and the broader linewidth of seed 2 may lead a higher SBS threshold than that value in seed 1 [30

30. P. Mitchell, A. Janssen, and J. K. Luo, “High performance laser linewidth broadening for stimulated Brillouin suppression with zero parasitic amplitude modulation,” J. Appl. Phys. 105(9), 93101–93104 (2009). [CrossRef]

]. Another reason is that the emission wavelength of laser diodes matches well with the optimal absorption wavelength of YDF when the pump power is higher (in case of seed 2), and therefore there is less unabsorbed pump light (which will be dumped by the pump dumper) and more output power. In order to gauge the SBS effect, we replace PDII.1 with a high precision power meter, and the backward powers as a function of pump power are recorded. Consider the coupling ration of the SMFC and the match error between the combiner and the YDF (The output fiber size of the combiner is a 15/130μm, the YDF size is 30/250μm), the backward power of the main amplifier is calibrated and results are also shown in Fig. 4 (green triangles curves). From the figures, it can be seen that the backward power starts to increase linearly up to an output power of about 85 W and 115 W when the amplifier chian is seed by seed 1 and seed 2, respectively. The maximum backward power in each single-frequency amplifier is of about 0.3W.

Second, we investigate the characteristic of the two-tone driven amplifier, shown in Fig. 5
Fig. 5 Power and spectrum characteristic of the two-tone driven amplifier chain (a) output power and backward power versus pump power, (b) spectrum in the amplifier chain.
. When seeded by a power ratio about 1:1.6, the highest output power of the main amplifier is 275.0 W at the limited pump power of 348.4W. The power conversion efficiency reaches 78.9%. The measured and calibrated backward power in the main amplifier is also shown in Fig. 5(a) (green triangles curves). It can be seen that maximum backward power is of about 0.19W, and there no nonlinearly up of he backward power is observed. Therefore, the output power is limited by the available pump power in experiment not by SBS, which predicts that by adding pump power, the output power of the amplifier can be further increased without remarkable SBS. In order to estimate whether there is beam quality degradation in the amplifier at high power operation, we recorded the beam profile when the output powers are 3.5W (when the main amplifier is off) and 275W, shown in the inserted pictures of Fig. 5(a). As we take measures such as by coiling of the YDF, water-cooling of the YDF and stripping the power in the inner cladding to ensure the main amplifier works at the fundamental mode, no obvious beam quality degradation is observed when the power is as high as 275W. The spectrum of the power amplifier are captured and shown in Fig. 5(b). When the output power is 275W in the main amplifier, the ASE is suppressed by ~30 dB. Although the SBS is suppressed, FWM appears when the output of the amplifier is 275W, shown in the insert diagram of Fig. 5(b). However, FWM effects are suppressed by over 15 dB, in correspondence with the prediction in reference [5

5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]

]. Moreover, as the power transferred into the FWM-sidebands propagates in forward direction, which will not lead to the damage of the low power element in the former stage amplifier. And FWM side-bands have not evidence influence on coherent combining of the multi-wavelength lasers.

Then, we investigate the characteristic of the multi-tone driven amplifier chain seeded by frequency modulated single-frequency laser, experimental results is shown in Fig. 6
Fig. 6 Power and spectrum characteristic of the multi-tone driven amplifier chain seed by frequency modulated single-frequency laser. (a) output power and backward power versus pump power, (b) spectrum in the amplifier chain, Frequency distribution of the frequency modulated laser before (c) and after (d) the amplifier chain.
. Figure 6(a) shows that the highest output power is ~275.0W at the ultimate pump power of 348.4W, with power conversion efficiency of 78.9%. Similar to the two-tone driven system, no obvious SBS effect is observed at the highest power and the output power is limited by the available pump power. The measured spectrum (Fig. 6(b)) shows that when the output power is 275W in the main amplifier, the ASE is suppressed by ~30 dB. Using an F-P interferometer (FPI100, fineness 400, FSR 4 GHz, Topica Inc), we measured the frequency distribution of the phase modulated single-frequency laser before and after the amplifier chain. In experiment, the modulation amplitude is pi/2 and modulation frequency is 100MHz, results are shown in Fig. 6(c) and 6(d). Figure 6(c) is frequency distribution before amplifier chain, it can be seen that there are 5 sidebands can be read clearly, result agree with the theory well. Figure 6(d) is frequency distribution measured from the power amplifier when the power is ~275W. Although the calculated linewidth of a single longitudinal mode before and after the amplifier chain are 7.3MHz and 9.2MHz, consider the linewidth resolution of the F-P interferometer is only about 10MHz, its make no sense to validate that there are any linewidth broadening effects. Therefore, results show that there are no linewidth broadening effects are observed in the amplified laser.

In two categories multi-tone driven amplifiers, the output power are more than 2.2 times and 1.6 times of that value when driven by seed 1 and seed 2, respectively. Experiment results indicate that scaling these systems to even higher power can be expected by increasing the pump power.

3.2 Phase locking of two multi-tone driven amplifier chains

3.2.1 Experiment setup of the phase locking of two multi-tone driven amplifier chains

Experimental setup of the phase locking of two multi-tone driven amplifier chains is shown in Fig. 7
Fig. 7 Experimental setup of phase locking of two multi-tone driven amplifier chains. MO: master oscillator, PM1, PM2: phase modulator, CO1, CO1: collimator, PD: photodetector.
. Two amplifier chains are used for phase locking. Channel 1 works at full power output of 275W. In channel 2, the output power is ~3.5W, as AIII.2 is power off for lacking of pumps. The laser beam from each amplifier is first collimated by a lens, and then sampled by a sampler. The reflected beam is collected by the power meter through a high reflect (HR) mirror. The transmission beam from the sampler is collected by a polarization maintained single-mode fiber through a focus lens. The single-mode fiber is used for pick-up the piston type wave-front (phase noise) of the laser in each amplifier, with a similar function in reference [31

31. J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007). [CrossRef] [PubMed]

]. Each collected beam is spitted into two beams by a 99:1 splitter, the main part of the beam is send to a fiber pigtailed collimator (CO). The diameter of laser beam output from the collimator is ~1.5mm. Tilt angle of the laser beams are carefully tuned to ensure the laser beams overlap with each other at the observing plane of the camera (SP620U, Ophir-spiricon Inc.). The collimated output beam array is sampled by a mirror. After the sampler, part of the beam is sent to a home-made pinhole with a radius of 50 μm, a photodetector is located immediately behind the pinhole. The location of the pinhole is carefully adjusted to ensure the maximum output of the detector. The optical power detected by the photodetector is defined as metric function J and will be used in SPGD algorithm. Another part of the beam after the sampler is sent to an infrared camera to diagnose the profile of the combined beam. In our experiment, SPGD algorithm is performed on digital signal processor (DSP) and phase control signals are sent to the phase modulators through digital to analogy (D/A) converters.

As the visibility is a periodic function of optical path difference Δl, in order to realize high visibility interference pattern, two step optical path and phase control should be carried out. Firstly, optical path difference is roughly tuned to ensure the high visibility interference pattern can be obtained. In our experiment, the optical path difference is controlled by cutting and fusion of the fibers and tuning of the optical path of each laser beams in the free space. Then, precisely phase control against the phase noise (phase locking) is implemented by the phase modulator using SPGD algorithm [15

15. P. Zhou, Z. Liu, X. Wang, Y. Ma, H. Ma, X. Xu, and S. Guo, “Coherent beam combining of fiber amplifiers using stochastic parallel gradient descent algorithm and its application,” IEEE J. Sel. Top. Quantum Electron. 15(2), 248–256 (2009). [CrossRef]

]. The steps for active phasing using SPGD algorithm can be briefly described as follows. Metric function J=J(u) is a function ofu, whereu=(u1,u2),ui is control signals applied to phase modulators. The algorithm is implemented in infinite iterations until ended manually. Each iteration cycle works as follows.

  • (1) Generate statistically independent random perturbations and convert to voltagesδu={δu1,δu2}, where all |δui| are small values that are typically chosen as statistically independent variables having zero mean and equal variances, δuk=0,δukδul=σ2δkl, δkl is the Kronecker symbol and σ2is the variance.
  • (2) Apply the control voltages on the phase modulators with the positive perturbations and get the metric functionJ+=J(u+δu), then apply the control voltages with the negative perturbations and get the metric functionJ=J(uδu).
  • (3) Calculate the difference between two evaluations of the metric functionδJ=J+J.
  • (4) Update the control voltagesui=ui+γδuiδJ, i = 1, 2, where γ is the updating gain, andγ>0 corresponds to the procedure of in-phase phase-locking of each channel.

3.2.2 Results of phase locking of two multi-tone driven amplifier chains

Firstly, phase locking of the two two-tone driven amplifier chains is studied. In experiment, we put the power supply and the power amplifiers in the same platform, the shake of the fans of the power supply is coupled into the optical fibers, and the phase difference between each amplifier chain fluctuate rapidly. Therefore, the metric function (J) fluctuates tempestuously (shown in first 0.9 s of Fig. 8(a)
Fig. 8 Results of phase locking for two-tone driven amplifier chains (a) metric function from open-loop to close-loop. (b) lineouts of the interference pattern in open-loop and closed-loop.
) between 0 V and 0.47 V. The measured frequency of the metric function in open-loop is more than 300Hz. When the SPGD algorithm is implemented and the system is in closed-loop, the main-lobe of the interference pattern is locking to the center despite of the phase noise, the dependence of J on time is larger than 0.4V for most of the time, shown in the last 0.9 s in Fig. 8(a). The calculated mean value of the metric function in closed-loop is of about 1.75 times of that value in open-loop. Lineouts of the one shoot of the interference pattern in open-loop and closed-loop of the amplified beams are shown in Fig. 8(b). Results show that the visibility is increased from 0 to 0.76 when the system evolves from open-loop to closed-loop.

Then, phase locking of the multi-tone driven amplifier chains seeded by frequency modulated single-frequency laser is realized. In order to avoid the phase noise induced by the shake of the power supplies, we separate the optical fibers of the amplifier chain and the power supply in different platform. The phase noise is therefore mitigated a lot and the measured phase noise frequency is less than 100Hz. When the SPGD algorithm is not implementing and the system is in open-loop, the depended of J on time is fluctuated between 0 V and 0.37 V, shown in the first 22.5 s of Fig. 9(a)
Fig. 9 Results of phase locking for multi-tone driven amplifier chain seeded by frequency modulated single-frequency laser (a) metric function from open-loop to closed-loop. (b) lineouts of the long exposure interference pattern in open-loop and closed-loop.
. When the SPGD algorithm is implemented and the system is in closed-loop, the dependence of J on time is larger than 0.3V for most of the time despite of the phase noise, shown in the last 22.5 s in Fig. 9(a).The calculated mean value of the metric function in closed-loop is of about 1.83 times of that value in open-loop. Corresponding lineouts of the long exposure interference pattern in open-loop and closed-loop are also shown in Fig. 9(b). The long exposure visibility is increased from 0 to 0.78 when the system evolves from open-loop to close loop.

4. Summary

In summary, we have demonstrated and phase locked two categories of multi-tone driven amplifiers. In theory, we reviewed the principle of multi-tone driven amplifier and investigated the principle of coherent beam combining of multi-tone lasers. In experiment, the SBS are all effectively suppressed in the two configurations and output powers are all increased a lot than a single-frequency driven amplifier. Scaling a single amplifier chain up to higher power by adding pump power without remarkable SBS in these two configurations is feasible. Phase locking of two multi-tone driven amplifier chains is implemented by using SPGD algorithm. Robust phase locking is realized despite the fluctuation of the phase noise difference in these two categories of multi-tone driven amplifiers. Coherent beam combing of multi-tone driven amplifiers may be a promising way for high power demonstration of fiber amplifiers. Scaling the system to higher power can be expected by increasing the power per fiber chain and adding the number of laser channels.

Acknowledgements

This work is supported by the Innovation Foundation for Graduates in National University of Defense Technology, China (Grant No. B080702).

References and links

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G. D. Goodno, L. D. Book, and J. E. Rothenberg, “Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier,” Opt. Lett. 34(8), 1204–1206 (2009). [CrossRef] [PubMed]

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V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31(2), 161–163 (2006). [CrossRef] [PubMed]

8.

A. Liu, “Suppressing stimulated Brillouin scattering in fiber amplifiers using nonuniform fiber and temperature gradient,” Opt. Express 15(3), 977–984 (2007). [CrossRef] [PubMed]

9.

I. Dajani, C. Zeringue, T. J. Bronder, T. Shay, A. Gavrielides, and R. Craig, “A theoretical treatment of two approaches to SBS mitigation with two-tone amplification,” Opt. Express 16(18), 14233–14247 (2008). [CrossRef] [PubMed]

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I. Dajani, C. Zeringue, C. Lu, C. Vergien, L. Henry, and C. Robin, “Stimulated Brillouin scattering suppression through laser gain competition: scalability to high power,” Opt. Lett. 35(18), 3114–3116 (2010). [CrossRef] [PubMed]

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G. D. Goodno, C. P. Asman, J. Anderegg, S. Brosnan, E. C. Cheung, D. Hammo, H. Injeyan, H. Komine, W. H. Long, M. Jr McClellan, S. J. McNau, S. Redmond, R. Simpson, J. Sollee, M. Weber, S. B. Weiss, and M. Wickham, “Brightness-scaling potential of actively phase-locked solid-state laser arrays,” IEEE J. Sel. Top. Quantum Electron. 13(3), 460–472 (2007). [CrossRef]

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L. Jianfeng, D. Kailiang, W. Yishan, Z. Wei, Z. Jianhua, and G. Yongkang, “High-power coherent beam combining of two photonic crystal fiber lasers,” IEEE Photon. Technol. Lett. 20(11), 888–890 (2008). [CrossRef]

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V. Jolivet, P. Bourdon, B. Bennai, L. Lombard, D. Goular, E. Pourtal, G. Canat, Y. Jaouen, B. Moreau, and O. Vasseur, “Beam shaping of single-mode and multimode fiber amplifier arrays for propagation through atmospheric turbulence,” IEEE J. Sel. Top. Quantum Electron. 15(2), 257–268 (2009). [CrossRef]

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M. A. Vorontsov, T. Weyrauch, L. A. Beresnev, G. W. Carhart, L. Liu, and K. Aschenbach, “Adaptive array of phase-locked fiber collimators analysis and experimental demonstration,” IEEE J. Sel. Top. Quantum Electron. 15(2), 269–280 (2009). [CrossRef]

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30.

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31.

J. Lhermite, A. Desfarges-Berthelemot, V. Kermene, and A. Barthelemy, “Passive phase locking of an array of four fiber amplifiers by an all-optical feedback loop,” Opt. Lett. 32(13), 1842–1844 (2007). [CrossRef] [PubMed]

OCIS Codes
(060.2630) Fiber optics and optical communications : Frequency modulation
(140.0140) Lasers and laser optics : Lasers and laser optics
(140.3280) Lasers and laser optics : Laser amplifiers
(140.3290) Lasers and laser optics : Laser arrays

ToC Category:
Lasers and Laser Optics

History
Original Manuscript: January 11, 2011
Revised Manuscript: March 12, 2011
Manuscript Accepted: March 22, 2011
Published: April 1, 2011

Citation
Xiaolin Wang, Jingyong Leng, Pu Zhou, Wenbo Du, Hu Xiao, Yanxing Ma, Xiaolin Dong, Xiaojun Xu, Zejin Liu, and Yijun Zhao, "Phase locking of a 275W high power all-fiber amplifier seeded by two categories of multi-tone lasers," Opt. Express 19, 7312-7324 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-8-7312


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References

  1. S. Gray, A. Liu, D. T. Walton, J. Wang, M. J. Li, X. Chen, A. B. Ruffin, J. A. DeMeritt, and L. A. Zenteno, “502 Watt, single transverse mode, narrow linewidth, bidirectionally pumped Yb-doped fiber amplifier,” Opt. Express 15(25), 17044–17050 (2007). [CrossRef] [PubMed]
  2. M. D. Mermelstein, K. Brar, M. J. Andrejco, A. D. Yablon, M. Fishteyn, C. Headley, and D. J. DiGiovanni, “All-fiber 194 W single-frequency single-mode Yb-doped master-oscillator power-amplifier,” Fiber Lasers V: Technology, Systems, and Applications, Jes Broeng and Clifford Headley eds. Proc. SPIE 6873, 68730L-1–68731L-6 (2008).
  3. Y. Jeong, J. Nilsson, J. K. Sahu, D. N. Payne, R. Horley, L. M. B. Hickey, and P. W. Turner, “Power scaling of single-frequency ytterbium-doped fiber master-oscillator power-amplifier sources up to 500 W,” IEEE J. Sel. Top. Quantum Electron. 13(3), 546–551 (2007). [CrossRef]
  4. G. D. Goodno, L. D. Book, and J. E. Rothenberg, “Low-phase-noise, single-frequency, single-mode 608 W thulium fiber amplifier,” Opt. Lett. 34(8), 1204–1206 (2009). [CrossRef] [PubMed]
  5. I. Dajani, C. Zeringue, and T. Shay, “Investigation of nonlinear effects in multitone-driven narrow-linewidth high-power amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(2), 406–414 (2009). [CrossRef]
  6. P. Wessels, P. Adel, M. Auerbach, D. Wandt, and C. Fallnich, “Novel suppression scheme for Brillouin scattering,” Opt. Express 12(19), 4443–4448 (2004). [CrossRef] [PubMed]
  7. V. I. Kovalev and R. G. Harrison, “Suppression of stimulated Brillouin scattering in high-power single-frequency fiber amplifiers,” Opt. Lett. 31(2), 161–163 (2006). [CrossRef] [PubMed]
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