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Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 19, Iss. 9 — Apr. 25, 2011
  • pp: 8656–8661
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Preferential gain photonic-crystal fiber for mode stabilization at high average powers

Tino Eidam, Steffen Hädrich, Florian Jansen, Fabian Stutzki, Jan Rothhardt, Henning Carstens, Cesar Jauregui, Jens Limpert, and Andreas Tünnermann  »View Author Affiliations


Optics Express, Vol. 19, Issue 9, pp. 8656-8661 (2011)
http://dx.doi.org/10.1364/OE.19.008656


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Abstract

We report on the design and experimental investigation of a preferential gain photonic-crystal fiber with a mode-field diameter of 47 µm. This few-mode fiber design confines the doping of Ytterbium-ions just to the center of the core and, therefore, promotes fundamental mode operation. In a chirped-pulse amplification system we extracted up to 303 W of average power from this fiber with a measured M2 value of 1.4.

© 2011 OSA

1. Introduction

Ultrashort pulse laser systems have found a large number of applications in science and industry for which, usually, an excellent beam quality and high pulse energies, peak powers and average powers are desirable. In recent years rapid progress has been made and impressive results have been achieved by using bulk Ti:Sapphire systems [1

1. I. Matsushima, H. Yashiro, and T. Tomie, “10 kHz 40 W Ti:sapphire regenerative ring amplifier,” Opt. Lett. 31(13), 2066–2068 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-13-2066. [CrossRef] [PubMed]

] or solid-state laser concepts like thin disk [2

2. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-13-2302. [CrossRef] [PubMed]

], slab [3

3. P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. 35(24), 4169–4171 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-24-4169. [CrossRef] [PubMed]

] or fiber [4

4. J. Limpert, F. Röser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. Jauregui, and A. Tünnermann, “High Repetition Rate Gigawatt Peak Power Fiber Laser Systems: Challenges, Design, and Experiment,” IEEE J. Sel. Top. Quantum Electron. 15(1), 159–169 (2009). [CrossRef]

], all based on Ytterbium doped active materials. Undoubtedly, every technology has its own advantages and drawbacks and, so far, none of them has achieved to fulfill simultaneously all the requirements stated above.

If it is not possible to use strictly single-mode fibers (a task almost impossible at large core sizes), one solution is to promote fundamental mode operation in few-mode fibers. This can be achieved by reducing the radius of the active area while the core size and, therefore, the MFDs are kept constant. Hence, due to this reduced doping area, the overlap of higher order modes with the gain region can be effectively reduced while the fundamental mode overlap is only slightly diminished. This way the fiber offers preferential gain to the fundamental mode.

In this paper we report on the first implementation of the preferential gain concept in a Photonic-Crystal Fiber (PCF). By incorporating this fiber with 1.7 m length and a MFD of 47 µm into a state-of-the-art fiber CPA system it was possible to extract 303 W of average power (212 W compressed) with 470 fs pulses and 106 µJ pulse energy.

2. Preferential gain fiber

Reducing the doping area in active fibers was already suggested more than 20 years ago [8

8. J. R. Armitage, “Three-level fiber laser amplifier: a theoretical model,” Appl. Opt. 27(23), 4831–4836 (1988), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-23-4831. [CrossRef] [PubMed]

]. The initial intention was to control the overlap of pump light propagating in a multimode core with the doped area and, consequently, to increase the pump absorption. Later, reducing the doped area was exploited in Erbium doped fibers in order to achieve preferential gain for the fundamental mode inside of a multimode signal core [9

9. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23(21), 1683–1685 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1683. [CrossRef]

, 10

10. J. M. Sousa and O. G. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74(11), 1528 (1999). [CrossRef]

]. This work triggered some theoretical studies aimed at investigating the optimum doping profiles and radii [11

11. T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, “Spatial dopant profiles for transverse-mode selection in multimode waveguides,” J. Opt. Soc. Am. B 19(7), 1539–1543 (2002), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-7-1539. [CrossRef]

, 12

12. J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009). [CrossRef]

] but, apart from a proof-of-principle experiment [13

13. J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. 35(11), 1828–1830 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-11-1828. [CrossRef] [PubMed]

], this type of fiber has found very little application in practice.

Here we apply the principle of preferential gain to a PCF, where it can be easily incorporated using the stack-and-draw production technique. The fiber used in our experiments is a rod-type PCF as shown in Fig. 1
Fig. 1 Scanning electron microscope image of the preferential gain PCF used in the experiments. Also depicted is a schematic diagram of the core region, where the pre-drawing positions of the different glass rods are shown.
. Air holes in the cladding with a hole-to-hole distance (pitch) of Λ = 11 µm and a relative hole size of d/Λ = 0.15 define a 19-missing-holes signal core. The resulting edge-to-edge diameter is 64 µm with a measured effective mode-field area of 1750 µm2 for the fundamental mode at 1030nm. This corresponds to a MFD of 47 µm. Due to this large MFD the fiber has to be kept straight in order to avoid bend-induced distortions and losses. Consequently, the fiber possesses a large outer diameter of 1.7 mm. No additional coating material is required, which greatly increases the high power capability of this fiber design. The air-clad diameter is 240 µm resulting in a pump signal absorption of 6 dB/m at 976 nm. Additionally, the positions of the different glass rods during the stacking process are depicted in Fig. 1.

It can be seen that only the inner 7 rods are made of Ytterbium-doped fused silica, whereas the remaining 12 core rods consist of pure fused silica. The refractive index of both types of glass are matched by nano-structuring the Ytterbium doped rods [14

14. W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Large mode area photonic crystal fibre laser,” in Conference on Lasers and Electro-Optics 2001, Vol. 56 of OSA Trends in Optics and Photonics Series (2001), paper CWC1.

]. Hereby, Ytterbium- and Fluorine-doped glass rods are mixed in a preceding stack-and-draw process resulting in a sub-wavelength scale structure with an average refractive index similar to that of pure fused silica. It can also be seen from Fig. 1 that the resulting ratio R of doped radius r doped and core radius r core is R = r doped/r core = 0.5. This value, in combination with the rectangular doping profile (assuming negligible diffusion during the drawing process), is very close to the optimum theoretical case of R = 0.5-0.6 [11

11. T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, “Spatial dopant profiles for transverse-mode selection in multimode waveguides,” J. Opt. Soc. Am. B 19(7), 1539–1543 (2002), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-7-1539. [CrossRef]

, 12

12. J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009). [CrossRef]

]. The existence of such an optimum can be understood since, on the one hand, an increase of the doping radius towards and beyond R = 1 results in an unwanted increase of gain for the higher order modes which have their highest intensity in the outer core region, like e.g. the LP11-mode. On the other hand, modes like the LP02 with their narrow intensity maximum in the center of the signal core are preferentially amplified should the value of R be too small.

Please note that, although this is a PCF, its guiding properties are close to those of a step-index fiber, since the cladding comprises a large number of small air holes. The cladding can, therefore, in a first approximation, be thought of as an equivalent region with an effective index slightly lower than that of the core. Therefore, the calculated modes are very similar to the analytical LPmn solution of step-index fibers [16

16. A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London 1983).

] and we will use this notation herein. It can be seen from this figure that for Δn > 0 the fundamental mode slowly evolves towards a flat-top profile which is accompanied by a small beam quality degradation. Only for too strong depressions does the fundamental mode become donut-shaped, which is usually unwanted. Therefore, a given Δn-value arising from production tolerances can limit the maximum achievable core diameter, since these mode deformations become more sensitive to index variations the larger the core sizes. However, to a small extent, the mode profiles can be controlled by a variation of the relative hole size d/Λ.

Drawbacks of using a smaller doped area are the reduction of gain, pump absorption and the lower extractable energy compared to a fiber with R = 1. For a fixed pump core diameter, which is usually defined by the available pump diode beam quality, this effect has to be compensated for by making the fiber longer or by increasing the doping concentration, although the latter is usually limited by the occurrence of photo-darkening [17

17. S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, “Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power,” Opt. Express 15(22), 14838–14843 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14838. [CrossRef] [PubMed]

]. However, in this particular case, the lower gain per meter offered by this fiber design is not necessarily a big drawback since this fiber will be typically used as the main amplifier where only moderate gains are required.

3. High power experiments

In order to prove the high power performance of the preferential gain PCF, we used 1.7 m of this fiber as main amplifier in the fiber CPA system presented in [6

6. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-255. [CrossRef] [PubMed]

]. In this system, femtosecond pulses at 1028 nm central wavelength and 76 MHz pulse repetition frequency are stretched to about 3 ns pulse duration by means of a dielectric-grating Öffner-type stretcher. After passing through a spatial light modulator (used to pre-compensate for the nonlinear phase acquired in the whole system) the pulse repetition frequency is reduced to 200 kHz using an acousto-optical modulator. After pre-amplification, nearly 20 W of average power, corresponding to a pulse energy of 10 µJ, are launched into the preferential gain main amplifier fiber. The PCF is pumped in counter-propagating direction with a pump diode emitting at 976 nm central wavelength. Figure 3
Fig. 3 Average output power and measured beam quality (averaged across both directions) of the main amplifier depending on the launched pump power. Additionally, a near-field image of the output beam at the maximum power level is shown in the inset.
shows the achieved output power and the corresponding beam quality as a function of the launched pump power (assuming 90% pump coupling efficiency into the fiber). The M2-values depicted in this figure were measured using the standard second-moments method and then averaged over both measured directions.

At a maximum launched pump power of 650 W an average output power of 303 W corresponding to 152 µJ of pulse energy could be achieved. It can be seen in Fig. 3 that by increasing the pump power, the beam quality steadily improves to a value of M2 = 1.4 at maximum power. This is the direct effect of the preferential gain principle: at low power operation the beam quality is worse due to the excitation of both the fundamental mode and a set of higher order modes; however, at larger powers, i.e with higher gain, the relative mode content of the higher order modes is continuously reduced due to their lower gain in comparison to the fundamental mode.

Pulse compression was achieved by means of a dielectric-grating compressor. We obtained an compressed average power of 212 W corresponding to 106 µJ of pulse energy. The spectrum measured with an optical spectrum analyzer is shown in Fig. 4a
Fig. 4 a) Spectrum at the output of the system measured with an optical spectrum analyzer b) Temporal pulse shape retrieved with a commercially available FROG device (1% FROG error). The inset shows the measured and retrieved FROG traces.
. The pulse shape depicted in Fig. 4b was measured using a commercially available FROG device. The pulse duration was measured to be 470 fs corresponding to a pulse peak power of 165 MW.

Further increase of the average power resulted in the onset of the mode-instabilities mentioned in the introduction. However, the average power threshold of this instability has been considerably increased in this fiber design when compared to other few-mode fiber designs (e.g [18

18. F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-24-3495. [CrossRef] [PubMed]

].).

4. Conclusion

It has been shown that reducing the doped area and exploiting the resulting effect of preferential gain can considerably increase the average power limit of short-length, large-core fibers. Preferential gain increases the mode-instability threshold originating from residual higher-order modes and provides a fundamental-mode operation even at large core sizes and average powers without bending of the fiber. We integrated, for the first time to our knowledge, this concept into a photonic-crystal fiber and we were able to extract more than 300 W of average power with a MFD of 47 µm and a nearly diffraction-limited beam by using it in a state-of-the-art CPA system. After compression we extracted pulses with 470 fs duration and 106 µJ pulse energy at an average power of 212 W. Although all these parameters alone are not an improvement in themselves, their combination is an important step towards high peak- and average power ultrashort pulse laser systems.

Further power scaling is feasible by incorporating the preferential-gain concept into sophisticated fiber designs that are “more” single-mode. Promising candidates are e.g. large-pitch fibers [15

15. F. Jansen, F. Stutzki, H.-J. Otto, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tünnermann, “The influence of index-depressions in core-pumped Yb-doped large pitch fibers,” Opt. Express 18(26), 26834–26842 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-26-26834. [CrossRef]

] that have already demonstrated their high-power capability [19

19. F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=ol-36-5-689. [CrossRef] [PubMed]

].

Acknowledgements

The research leading to these results has received funding from the European Research Council under the European Union's Seventh Framework Programme (FP7/2007-2013) / ERC Grant agreement n° [240460] and the Thuringian Ministry of Education, Science and Culture under contract PE203-2-1 (MOFA). S.H. acknowledges financial support by the Carl Zeiss Stiftung, Germany. F. J. acknowledges financial support by the Abbe School of Photonics Jena.

References and links

1.

I. Matsushima, H. Yashiro, and T. Tomie, “10 kHz 40 W Ti:sapphire regenerative ring amplifier,” Opt. Lett. 31(13), 2066–2068 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-13-2066. [CrossRef] [PubMed]

2.

C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-13-2302. [CrossRef] [PubMed]

3.

P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. 35(24), 4169–4171 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-24-4169. [CrossRef] [PubMed]

4.

J. Limpert, F. Röser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. Jauregui, and A. Tünnermann, “High Repetition Rate Gigawatt Peak Power Fiber Laser Systems: Challenges, Design, and Experiment,” IEEE J. Sel. Top. Quantum Electron. 15(1), 159–169 (2009). [CrossRef]

5.

T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-2-94. [CrossRef] [PubMed]

6.

T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-255. [CrossRef] [PubMed]

7.

C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258. [CrossRef] [PubMed]

8.

J. R. Armitage, “Three-level fiber laser amplifier: a theoretical model,” Appl. Opt. 27(23), 4831–4836 (1988), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-23-4831. [CrossRef] [PubMed]

9.

H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23(21), 1683–1685 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1683. [CrossRef]

10.

J. M. Sousa and O. G. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74(11), 1528 (1999). [CrossRef]

11.

T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, “Spatial dopant profiles for transverse-mode selection in multimode waveguides,” J. Opt. Soc. Am. B 19(7), 1539–1543 (2002), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-7-1539. [CrossRef]

12.

J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009). [CrossRef]

13.

J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. 35(11), 1828–1830 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-11-1828. [CrossRef] [PubMed]

14.

W. J. Wadsworth, J. C. Knight, and P. St. J. Russell, “Large mode area photonic crystal fibre laser,” in Conference on Lasers and Electro-Optics 2001, Vol. 56 of OSA Trends in Optics and Photonics Series (2001), paper CWC1.

15.

F. Jansen, F. Stutzki, H.-J. Otto, M. Baumgartl, C. Jauregui, J. Limpert, and A. Tünnermann, “The influence of index-depressions in core-pumped Yb-doped large pitch fibers,” Opt. Express 18(26), 26834–26842 (2010), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-26-26834. [CrossRef]

16.

A. W. Snyder, and J. D. Love, Optical Waveguide Theory (Chapman and Hall, London 1983).

17.

S. Jetschke, S. Unger, U. Röpke, and J. Kirchhof, “Photodarkening in Yb doped fibers: experimental evidence of equilibrium states depending on the pump power,” Opt. Express 15(22), 14838–14843 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-22-14838. [CrossRef] [PubMed]

18.

F. Röser, T. Eidam, J. Rothhardt, O. Schmidt, D. N. Schimpf, J. Limpert, and A. Tünnermann, “Millijoule pulse energy high repetition rate femtosecond fiber chirped-pulse amplification system,” Opt. Lett. 32(24), 3495–3497 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=ol-32-24-3495. [CrossRef] [PubMed]

19.

F. Stutzki, F. Jansen, T. Eidam, A. Steinmetz, C. Jauregui, J. Limpert, and A. Tünnermann, “High average power large-pitch fiber amplifier with robust single-mode operation,” Opt. Lett. 36(5), 689–691 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=ol-36-5-689. [CrossRef] [PubMed]

OCIS Codes
(060.2280) Fiber optics and optical communications : Fiber design and fabrication
(140.7090) Lasers and laser optics : Ultrafast lasers

ToC Category:
Fiber Optics and Optical Communications

History
Original Manuscript: January 31, 2011
Revised Manuscript: March 14, 2011
Manuscript Accepted: March 15, 2011
Published: April 19, 2011

Citation
Tino Eidam, Steffen Hädrich, Florian Jansen, Fabian Stutzki, Jan Rothhardt, Henning Carstens, Cesar Jauregui, Jens Limpert, and Andreas Tünnermann, "Preferential gain photonic-crystal fiber for mode stabilization at high average powers," Opt. Express 19, 8656-8661 (2011)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-9-8656


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References

  1. I. Matsushima, H. Yashiro, and T. Tomie, “10 kHz 40 W Ti:sapphire regenerative ring amplifier,” Opt. Lett. 31(13), 2066–2068 (2006), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-31-13-2066 . [CrossRef] [PubMed]
  2. C. R. E. Baer, C. Kränkel, C. J. Saraceno, O. H. Heckl, M. Golling, R. Peters, K. Petermann, T. Südmeyer, G. Huber, and U. Keller, “Femtosecond thin-disk laser with 141 W of average power,” Opt. Lett. 35(13), 2302–2304 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-13-2302 . [CrossRef] [PubMed]
  3. P. Russbueldt, T. Mans, J. Weitenberg, H. D. Hoffmann, and R. Poprawe, “Compact diode-pumped 1.1 kW Yb:YAG Innoslab femtosecond amplifier,” Opt. Lett. 35(24), 4169–4171 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-24-4169 . [CrossRef] [PubMed]
  4. J. Limpert, F. Röser, D. N. Schimpf, E. Seise, T. Eidam, S. Hädrich, J. Rothhardt, C. Jauregui, and A. Tünnermann, “High Repetition Rate Gigawatt Peak Power Fiber Laser Systems: Challenges, Design, and Experiment,” IEEE J. Sel. Top. Quantum Electron. 15(1), 159–169 (2009). [CrossRef]
  5. T. Eidam, S. Hanf, E. Seise, T. V. Andersen, T. Gabler, C. Wirth, T. Schreiber, J. Limpert, and A. Tünnermann, “Femtosecond fiber CPA system emitting 830 W average output power,” Opt. Lett. 35(2), 94–96 (2010), http://www.opticsinfobase.org/ol/abstract.cfm?URI=ol-35-2-94 . [CrossRef] [PubMed]
  6. T. Eidam, J. Rothhardt, F. Stutzki, F. Jansen, S. Hädrich, H. Carstens, C. Jauregui, J. Limpert, and A. Tünnermann, “Fiber chirped-pulse amplification system emitting 3.8 GW peak power,” Opt. Express 19(1), 255–260 (2011), http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-19-1-255 . [CrossRef] [PubMed]
  7. C. Jauregui, T. Eidam, J. Limpert, and A. Tünnermann, “The impact of modal interference on the beam quality of high-power fiber amplifiers,” Opt. Express 19(4), 3258–3271 (2011), http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-4-3258 . [CrossRef] [PubMed]
  8. J. R. Armitage, “Three-level fiber laser amplifier: a theoretical model,” Appl. Opt. 27(23), 4831–4836 (1988), http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-27-23-4831 . [CrossRef] [PubMed]
  9. H. L. Offerhaus, N. G. Broderick, D. J. Richardson, R. Sammut, J. Caplen, and L. Dong, “High-energy single-transverse-mode Q-switched fiber laser based on a multimode large-mode-area erbium-doped fiber,” Opt. Lett. 23(21), 1683–1685 (1998), http://www.opticsinfobase.org/abstract.cfm?URI=ol-23-21-1683 . [CrossRef]
  10. J. M. Sousa and O. G. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74(11), 1528 (1999). [CrossRef]
  11. T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, “Spatial dopant profiles for transverse-mode selection in multimode waveguides,” J. Opt. Soc. Am. B 19(7), 1539–1543 (2002), http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-19-7-1539 . [CrossRef]
  12. J. R. Marciante, “Gain Filtering for Single-Spatial-Mode Operation of Large-Mode-Area Fiber Amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15(1), 30–36 (2009). [CrossRef]
  13. J. R. Marciante, R. G. Roides, V. V. Shkunov, and D. A. Rockwell, “Near-diffraction-limited operation of step-index large-mode-area fiber lasers via gain filtering,” Opt. Lett. 35(11), 1828–1830 (2010), http://www.opticsinfobase.org/abstract.cfm?URI=ol-35-11-1828 . [CrossRef] [PubMed]
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