Abstract

0.5% Holmium (Ho) doped YAG single crystal fiber (SCF) was fabricated using Laser Heated Pedestal Growth (LHPG) method and characterized for its optical absorption and emission properties involving transitions between the 5I8 and 5I7 energy levels. The results verified the absorption peaks suitable for in-band direct pumping at 1908 nm and 1932 nm with the emission occurring between 2050 and 2150 nm. Small signal gain measurements were also performed for demonstrating the fiber like characteristics of the SCF.

© 2014 Optical Society of America

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    [CrossRef]
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  20. S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
    [CrossRef]
  21. M. Schellhorn and A. Hirth, “Modeling of intracavity-pumped quasi-three-level lasers,” IEEE J. Quantum Electron. 38(11), 1455–1464 (2002).
    [CrossRef]
  22. M. Digonnet, “Theory of superfluorescent fiber lasers,” J. Lightwave Technol. 4(11), 1631–1639 (1986).
    [CrossRef]
  23. J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
    [CrossRef]

2013 (1)

2012 (5)

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

X. Délen, S. Piehler, J. Didierjean, N. Aubry, A. Voss, M. A. Ahmed, T. Graf, F. Balembois, and P. Georges, “250 W single-crystal fiber Yb:YAG laser,” Opt. Lett. 37(14), 2898–2900 (2012).
[CrossRef] [PubMed]

N. Ter-Gabrielyan, V. Fromzel, X. Mu, H. Meissner, and M. Dubinskii, “High efficiency, resonantly diode pumped, double-clad, Er:YAG-core, waveguide laser,” Opt. Express 20(23), 25554–25561 (2012).
[CrossRef] [PubMed]

D. C. Brown, V. Envid, and J. Zembek, “Ho:YAG absorption cross sections from 1700 to 2200 nm at 83, 175, and 295 K,” Appl. Opt. 51(34), 8147–8158 (2012).
[CrossRef] [PubMed]

2011 (2)

X. Délen, I. Martial, J. Didierjean, N. Aubry, D. Sangla, F. Balembois, and P. Georges, “34 W continuous wave Nd:YAG single crystal fiber laser emitting at 946 nm,” Appl. Phys. B 104(1), 1–4 (2011).
[CrossRef]

P. C. Shi, I. A. Watson, and J. H. Sharp, “High-concentration Er:YAG single-crystal fibers grown by laser-heated pedestal growth technique,” Opt. Lett. 36(12), 2182–2184 (2011).
[CrossRef] [PubMed]

2010 (2)

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Q. Dong, G. Zhao, J. Chen, Y. Ding, and C. Zhao, “Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal,” J. Appl. Phys. 108(2), 023108 (2010).
[CrossRef]

2009 (2)

B. Walsh, “Review of Tm and Ho materials; spectroscopy and lasers,” Laser Phys. 19(4), 855–866 (2009).
[CrossRef]

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

2008 (1)

2002 (1)

M. Schellhorn and A. Hirth, “Modeling of intracavity-pumped quasi-three-level lasers,” IEEE J. Quantum Electron. 38(11), 1455–1464 (2002).
[CrossRef]

1997 (1)

1992 (1)

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

1991 (1)

R. S. F. Chang, S. Sengupta, L. B. Shaw, and N. Djeu, “Fabrication of laser materials by laser-heated pedestal growth,” Proc. SPIE 1410, 125–132 (1991).
[CrossRef]

1989 (1)

D. H. Jundt, M. M. Fejer, and R. L. Byer, “Characterization of single-crystal sapphire fibers for optical power delivery systems,” Appl. Phys. Lett. 55(21), 2170–2172 (1989).
[CrossRef]

1987 (1)

M. J. F. Digonnet, C. J. Gaeta, D. O’Meara, and H. J. Shaw, “Clad Nd:YAG fibers for laser applications,” J. Lightwave Technol. 5(5), 642–646 (1987).
[CrossRef]

1986 (2)

R. S. Feigelson, “Pulling optical fibers,” J. Cryst. Growth 79(1-3), 669–680 (1986).
[CrossRef]

M. Digonnet, “Theory of superfluorescent fiber lasers,” J. Lightwave Technol. 4(11), 1631–1639 (1986).
[CrossRef]

Ahmed, M. A.

Aubry, N.

Balembois, F.

Brown, D. C.

Byer, R. L.

D. H. Jundt, M. M. Fejer, and R. L. Byer, “Characterization of single-crystal sapphire fibers for optical power delivery systems,” Appl. Phys. Lett. 55(21), 2170–2172 (1989).
[CrossRef]

Chang, R. S. F.

R. S. F. Chang, S. Sengupta, L. B. Shaw, and N. Djeu, “Fabrication of laser materials by laser-heated pedestal growth,” Proc. SPIE 1410, 125–132 (1991).
[CrossRef]

Chase, L. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

Chen, J.

Q. Dong, G. Zhao, J. Chen, Y. Ding, and C. Zhao, “Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal,” J. Appl. Phys. 108(2), 023108 (2010).
[CrossRef]

Chen, P. Y.

Cheng, X. J.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Délen, X.

Didierjean, J.

Digonnet, M.

M. Digonnet, “Theory of superfluorescent fiber lasers,” J. Lightwave Technol. 4(11), 1631–1639 (1986).
[CrossRef]

Digonnet, M. J. F.

M. J. F. Digonnet, C. J. Gaeta, D. O’Meara, and H. J. Shaw, “Clad Nd:YAG fibers for laser applications,” J. Lightwave Technol. 5(5), 642–646 (1987).
[CrossRef]

Ding, Y.

Q. Dong, G. Zhao, J. Chen, Y. Ding, and C. Zhao, “Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal,” J. Appl. Phys. 108(2), 023108 (2010).
[CrossRef]

Djeu, N.

R. S. F. Chang, S. Sengupta, L. B. Shaw, and N. Djeu, “Fabrication of laser materials by laser-heated pedestal growth,” Proc. SPIE 1410, 125–132 (1991).
[CrossRef]

Dong, Q.

Q. Dong, G. Zhao, J. Chen, Y. Ding, and C. Zhao, “Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal,” J. Appl. Phys. 108(2), 023108 (2010).
[CrossRef]

Dubinskii, M.

Envid, V.

Feigelson, R. S.

R. S. Feigelson, “Pulling optical fibers,” J. Cryst. Growth 79(1-3), 669–680 (1986).
[CrossRef]

Fejer, M. M.

D. H. Jundt, M. M. Fejer, and R. L. Byer, “Characterization of single-crystal sapphire fibers for optical power delivery systems,” Appl. Phys. Lett. 55(21), 2170–2172 (1989).
[CrossRef]

Fromzel, V.

Fuhrberg, P.

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

Gaeta, C. J.

M. J. F. Digonnet, C. J. Gaeta, D. O’Meara, and H. J. Shaw, “Clad Nd:YAG fibers for laser applications,” J. Lightwave Technol. 5(5), 642–646 (1987).
[CrossRef]

Georges, P.

Gorajek, L.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Graf, T.

Harrington, J. A.

Hirth, A.

M. Schellhorn and A. Hirth, “Modeling of intracavity-pumped quasi-three-level lasers,” IEEE J. Quantum Electron. 38(11), 1455–1464 (2002).
[CrossRef]

Hönninger, C.

Hsu, K. Y.

Huang, K. Y.

Huang, S. L.

Jabczynski, J.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Jelinkova, H.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Jheng, D. Y.

Jiang, B. X.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Jundt, D. H.

D. H. Jundt, M. M. Fejer, and R. L. Byer, “Characterization of single-crystal sapphire fibers for optical power delivery systems,” Appl. Phys. Lett. 55(21), 2170–2172 (1989).
[CrossRef]

Koopmann, P.

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

Koranda, P.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Krupke, W. F.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

Kumar, G. A.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Kway, W. L.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

Kwiatkowski, J.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Lamrini, S.

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

Li, J.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Liu, W. B.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Martial, I.

X. Délen, Y. Zaouter, I. Martial, N. Aubry, J. Didierjean, C. Hönninger, E. Mottay, F. Balembois, and P. Georges, “Yb:YAG single crystal fiber power amplifier for femtosecond sources,” Opt. Lett. 38(2), 109–111 (2013).
[CrossRef] [PubMed]

X. Délen, I. Martial, J. Didierjean, N. Aubry, D. Sangla, F. Balembois, and P. Georges, “34 W continuous wave Nd:YAG single crystal fiber laser emitting at 946 nm,” Appl. Phys. B 104(1), 1–4 (2011).
[CrossRef]

Meissner, H.

Mottay, E.

Mu, X.

Nemec, M.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Nubling, R. K.

O’Meara, D.

M. J. F. Digonnet, C. J. Gaeta, D. O’Meara, and H. J. Shaw, “Clad Nd:YAG fibers for laser applications,” J. Lightwave Technol. 5(5), 642–646 (1987).
[CrossRef]

Pan, Y. B.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Payne, S. A.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

Piehler, S.

Pokhrel, M.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Samuel, P.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Sangla, D.

X. Délen, I. Martial, J. Didierjean, N. Aubry, D. Sangla, F. Balembois, and P. Georges, “34 W continuous wave Nd:YAG single crystal fiber laser emitting at 946 nm,” Appl. Phys. B 104(1), 1–4 (2011).
[CrossRef]

Sardar, D. K.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Schäfer, M.

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

Schellhorn, M.

M. Schellhorn and A. Hirth, “Modeling of intracavity-pumped quasi-three-level lasers,” IEEE J. Quantum Electron. 38(11), 1455–1464 (2002).
[CrossRef]

Scholle, K.

S. Lamrini, P. Koopmann, M. Schäfer, K. Scholle, and P. Fuhrberg, “Efficient high-power Ho:YAG laser directly in-band pumped by a GaSb-based laser diode stack at 1.9 μm,” Appl. Phys. B 106(2), 315–319 (2012).
[CrossRef]

Sengupta, S.

R. S. F. Chang, S. Sengupta, L. B. Shaw, and N. Djeu, “Fabrication of laser materials by laser-heated pedestal growth,” Proc. SPIE 1410, 125–132 (1991).
[CrossRef]

Sharp, J. H.

Shaw, H. J.

M. J. F. Digonnet, C. J. Gaeta, D. O’Meara, and H. J. Shaw, “Clad Nd:YAG fibers for laser applications,” J. Lightwave Technol. 5(5), 642–646 (1987).
[CrossRef]

Shaw, L. B.

R. S. F. Chang, S. Sengupta, L. B. Shaw, and N. Djeu, “Fabrication of laser materials by laser-heated pedestal growth,” Proc. SPIE 1410, 125–132 (1991).
[CrossRef]

Shi, P. C.

Smith, L. K.

S. A. Payne, L. L. Chase, L. K. Smith, W. L. Kway, and W. F. Krupke, “Infrared cross-section measurements for crystals doped with Er3+, Tm3+, and Ho3+,” IEEE J. Quantum Electron. 28(11), 2619–2630 (1992).
[CrossRef]

Sulc, J.

J. Kwiatkowski, J. Jabczynski, L. Gorajek, W. Zendzian, H. Jelinkova, J. Sulc, M. Nemec, and P. Koranda, “Resonantly pumped tunable Ho:YAG laser,” Laser Phys. Lett. 6(7), 531–534 (2009).
[CrossRef]

Ter-Gabrielyan, N.

Ueda, K. I.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Voss, A.

Walsh, B.

B. Walsh, “Review of Tm and Ho materials; spectroscopy and lasers,” Laser Phys. 19(4), 855–866 (2009).
[CrossRef]

Wang, L.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Watson, I. A.

Xu, J. Q.

W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
[CrossRef]

Yagi, H.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Yanagitani, T.

G. A. Kumar, M. Pokhrel, D. K. Sardar, P. Samuel, K. I. Ueda, T. Yanagitani, and H. Yagi, “2.1 μm emission spectral properties of Tm and Ho doped transparent YAG ceramic,” Sci. Adv. Mater. 4(5), 617–622 (2012).
[CrossRef]

Yeh, P. S.

Zaouter, Y.

Zembek, J.

Zendzian, W.

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[CrossRef]

Zhao, G.

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[CrossRef]

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W. X. Zhang, J. Zhou, W. B. Liu, J. Li, L. Wang, B. X. Jiang, Y. B. Pan, X. J. Cheng, and J. Q. Xu, “Fabrication, properties and laser performance of Ho:YAG transparent ceramic,” J. Alloy. Comp. 506(2), 745–748 (2010).
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[CrossRef]

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Q. Dong, G. Zhao, J. Chen, Y. Ding, and C. Zhao, “Growth and anisotropic thermal properties of biaxial Ho:YAlO3 crystal,” J. Appl. Phys. 108(2), 023108 (2010).
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Figures (7)

Fig. 1
Fig. 1

(a) Overview of the LHPG apparatus, including CO2 laser, reflaxicon optics, LaserMic, source rod, and fiber, and (b) Schematic diagram of the molten zone with CO2 laser beam contact at 360°.

Fig. 2
Fig. 2

(a) SEM image of the polished end-facet of the Ho:YAG SCF. (b) SEM image of the side of the sample showing the shallow grooves.

Fig. 3
Fig. 3

The absorption spectrum of the Ho:YAG SCF. (Inset) The measured incident laser beam size with respect to the distance from the focusing lens.

Fig. 4
Fig. 4

The absorption (red) and emission (green) cross section of the Ho:YAG SCF. The emission cross section is calculated from the measured absorption spectrum using McCumber Theory. The blue markers are measured gain for different wavelengths; see detailed descriptions in section 5.

Fig. 5
Fig. 5

The measured emission spectrum under different pump power using 1932.2 nm direct in-band pumping.

Fig. 6
Fig. 6

Small signal gain measurement setup. DM, dichroic mirror, highly reflective at 1932 nm. L1, L2, L3, L4, collimating and focusing lenses. L1 is AR-coated and the losses of L2-L4 are taken into as well as the Fresnel reflection on both end-facets of the SCF.

Fig. 7
Fig. 7

Small signal gain with increasing pump power for three different seed power. Empty markers, experiment data. Colored lines, simulation curves.

Tables (1)

Tables Icon

Table 1 Properties of glass, sapphire and YAG. Tp, melting temperature [12].

Equations (5)

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σ abs = α N ,
σ emi = σ abs Z lower Z upper exp( h v 0 hv kT ).
σ g =β σ emi (1β) σ abs
g eff = g 0 1+ P P sat
I sat = hv ( σ emi + σ abs )τ

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