Abstract

Using a beam propagation model of Yb3+ doped, CW fiber amplifiers we show that gain saturation by a strong fundamental mode significantly suppresses the growth of higher order modes with parallel polarization, but enhances the growth of higher order modes with perpendicular polarization. We quantify this effect in straight and bent fibers, with full core or restricted area doping.

© 2011 OSA

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References

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  1. A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 10180–10192 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-11-10180 .
    [CrossRef] [PubMed]
  2. J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
    [CrossRef]
  3. R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. QE-15, 1157–1161 (1979).
    [CrossRef]
  4. Z. Jiang and J. R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B 25, 247–254 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=josab-25-2-247 .
    [CrossRef]
  5. S. Liao, M. Gong, and H. Zhang, “Influence of mode distortion on the transverse mode competition in large-mode-area amplifiers,” Opt. Commun. 282, 406–412 (2009), http://linkinghub.elsevier.com/retrieve/pii/S0030401808010067 .
    [CrossRef]
  6. J. Marciante, “Gain filtering for single-spatial-mode operation of large-mode-area fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 30–36 (2009), http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4773298 .
    [CrossRef]
  7. S. Liao, M. Gong, and H. Zhang, “Theoretical calculation of beam quality factor of large-mode-area fiber amplifiers,” Laser Phys. 19, 437–444 (2009), http://www.springerlink.com/index/10.1134/S1054660X09030141 .
    [CrossRef]
  8. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15, 3236–3246 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3236 .
    [CrossRef] [PubMed]
  9. T. Bhutta, J. I. Mackenzie, D. P. Shepherd, and R. J. Beach, “Spatial dopant profiles for transverse-mode selection in multi-mode waveguides,” J. Opt. Soc. Am. B 19, 1539–1543 (2002), http://www.opticsinfobase.org/abstract.cfm?URI=josab-19-7-1539 .
    [CrossRef]
  10. J. Sousa and O. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
    [CrossRef]
  11. N. Andermahr and C. Fallnich, “Interaction of transverse modes in a single-frequency few-mode fiber amplifier caused by local gain saturation,” Opt. Express 16, 8678–8684 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-8678 .
    [CrossRef] [PubMed]
  12. N. Andermahr and C. Fallnich, “Modeling of transverse mode interaction in large-mode-area fiber amplifiers.” Opt. Express 16, 20038–20046 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-20038 .
    [CrossRef] [PubMed]
  13. D. Vysotsky and A. Napartovich, “Mode competition in steady-state optical waveguide amplifiers,” J. Exp. Theor. Phys. 108, 547–556 (2009). http://dx.doi.org/10.1134/S1063776109040013 .
    [CrossRef]
  14. J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Gaalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-7233 .
    [CrossRef] [PubMed]
  15. T. Eidam, S. Hadrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tunnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19, 8656–8661 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-9-8656 .
    [CrossRef] [PubMed]
  16. D. Marcuse, Theory of Dielectric Optical Waveguides , 2nd ed. (Academic Press, 1991).
  17. J. Koplow, D. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-7-442 .
    [CrossRef]

2005 (1)

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

1999 (1)

J. Sousa and O. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

1979 (1)

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. QE-15, 1157–1161 (1979).
[CrossRef]

Berdine, R. W.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Marcuse, D.

D. Marcuse, Theory of Dielectric Optical Waveguides , 2nd ed. (Academic Press, 1991).

Okhotnikov, O.

J. Sousa and O. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

Roh, W. B

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Russell, T. H.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Sanchez, A. D.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Shay, T. M.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Sousa, J.

J. Sousa and O. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

Spring, J. B.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Stolen, R. H.

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. QE-15, 1157–1161 (1979).
[CrossRef]

Ward, B. G.

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Appl. Phys. Lett. (1)

J. Sousa and O. Okhotnikov, “Multimode Er-doped fiber for single-transverse-mode amplification,” Appl. Phys. Lett. 74, 1528–1530 (1999).
[CrossRef]

IEEE J. Quantum Electron. (1)

R. H. Stolen, “Polarization effects in fiber Raman and Brillouin lasers,” IEEE J. Quantum Electron. QE-15, 1157–1161 (1979).
[CrossRef]

Proc. SPIE (1)

J. B. Spring, T. H. Russell, T. M. Shay, R. W. Berdine, A. D. Sanchez, B. G. Ward, and W. B Roh, “Comparison of stimulated Brillouin scattering thresholds and spectra in nonpolarization-maintaining and polarization-maintaining passive fibers,” Proc. SPIE 5709, 147–156 (2005).
[CrossRef]

Other (14)

A. V. Smith and J. J. Smith, “Mode instability in high power fiber amplifiers,” Opt. Express 19, 10180–10192 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-11-10180 .
[CrossRef] [PubMed]

Z. Jiang and J. R. Marciante, “Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers,” J. Opt. Soc. Am. B 25, 247–254 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=josab-25-2-247 .
[CrossRef]

S. Liao, M. Gong, and H. Zhang, “Influence of mode distortion on the transverse mode competition in large-mode-area amplifiers,” Opt. Commun. 282, 406–412 (2009), http://linkinghub.elsevier.com/retrieve/pii/S0030401808010067 .
[CrossRef]

J. Marciante, “Gain filtering for single-spatial-mode operation of large-mode-area fiber amplifiers,” IEEE J. Sel. Top. Quantum Electron. 15, 30–36 (2009), http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=4773298 .
[CrossRef]

S. Liao, M. Gong, and H. Zhang, “Theoretical calculation of beam quality factor of large-mode-area fiber amplifiers,” Laser Phys. 19, 437–444 (2009), http://www.springerlink.com/index/10.1134/S1054660X09030141 .
[CrossRef]

M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, “Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers,” Opt. Express 15, 3236–3246 (2007), http://www.opticsinfobase.org/abstract.cfm?URI=oe-15-6-3236 .
[CrossRef] [PubMed]

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

N. Andermahr and C. Fallnich, “Interaction of transverse modes in a single-frequency few-mode fiber amplifier caused by local gain saturation,” Opt. Express 16, 8678–8684 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-12-8678 .
[CrossRef] [PubMed]

N. Andermahr and C. Fallnich, “Modeling of transverse mode interaction in large-mode-area fiber amplifiers.” Opt. Express 16, 20038–20046 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-24-20038 .
[CrossRef] [PubMed]

D. Vysotsky and A. Napartovich, “Mode competition in steady-state optical waveguide amplifiers,” J. Exp. Theor. Phys. 108, 547–556 (2009). http://dx.doi.org/10.1134/S1063776109040013 .
[CrossRef]

J. W. Nicholson, A. D. Yablon, S. Ramachandran, and S. Gaalmi, “Spatially and spectrally resolved imaging of modal content in large-mode-area fibers,” Opt. Express 16, 7233–7243 (2008), http://www.opticsinfobase.org/abstract.cfm?URI=oe-16-10-7233 .
[CrossRef] [PubMed]

T. Eidam, S. Hadrich, F. Jansen, F. Stutzki, J. Rothhardt, H. Carstens, C. Jauregui, J. Limpert, and A. Tunnermann, “Preferential gain photonic-crystal fiber for mode stabilization at high average powers,” Opt. Express 19, 8656–8661 (2011). http://www.opticsinfobase.org/abstract.cfm?URI=oe-19-9-8656 .
[CrossRef] [PubMed]

D. Marcuse, Theory of Dielectric Optical Waveguides , 2nd ed. (Academic Press, 1991).

J. Koplow, D. Kliner, and L. Goldberg, “Single-mode operation of a coiled multimode fiber amplifier,” Opt. Lett. 25, 442–444 (2000), http://www.opticsinfobase.org/abstract.cfm?URI=ol-25-7-442 .
[CrossRef]

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Figures (6)

Fig. 1
Fig. 1

Mode irradiance profiles in straight fiber (top) and fiber bent to 50 mm radius (bottom). We call them m1 (left), m2 (center), and m6 (right).

Fig. 2
Fig. 2

Baseline model results for co-pumped amplifier (top) and counter-pumped amplifier (bottom) using the parameters in Table 1. Higher order modal input powers are set to zero.

Fig. 3
Fig. 3

Power in m2|| (solid) or m2 (dashed) or the sum of m2|| and m2 (chain) divided by power in m1 for a co-pumped amplifier (top) and a counter-pumped amplifier (bottom). The fiber is straight and the full core is doped. For the non-PM fiber the m2 power is launched half in each polarization, and the fields for the two polarizations of m2 are swapped every 20 mm. Other properties are listed in Table 1 and Fig. 1, and the pump and m1 powers are nearly identical to those in Fig. 2.

Fig. 4
Fig. 4

Ratio of power in m2|| to power in m1 for P s 1 = 300 W and P s 2 = 3 W . The beat length is 3.63 mm for these two modes. Depending on the phase between the two modes, m2|| growth relative to m1 is either positive or negative, but the net change in this ratio over a full cycle is negative.

Fig. 5
Fig. 5

A comparison of the relative gains vs. doping diameter for co-pumping. Other parameters are listed in Table 1. The gain G m is the output power divided by the input power in the m th mode. The upper plot is the gain of modes m2 and m2|| relative to m1; the lower is the gain of modes m6 and m6|| relative to m1. For non-PM fiber the gain of mode 2 is reasonably approximated by the geometric mean of the two curves shown.

Fig. 6
Fig. 6

A comparison of the relative gain vs. doping diameter for fiber bent to a radius of 50 mm in co-pumped amplifier (see Fig. 1 for bent fiber mode profiles). Other parameters are listed in Table 1. The gain G m is the output power divided by the input power in the m th mode. The upper plot is the gain of modes m2 and m2|| relative to m1; the lower is the gain of modes m6 and m6|| relative to m1. For non-PM fiber the gain of mode 2 is reasonably approximated by the geometric mean of the two curves shown.

Tables (1)

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Table 1 Parameters of Test Amplifier

Equations (4)

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n u ( x , y ) = P p σ p a / h ν p A + I s σ s a / h ν s P p ( σ p a + σ p e ) / h ν p A + I s ( σ s a + σ s e ) / h ν s + 1 / τ ,
d P p d z = P p A ( σ p e n u σ p a n l ) N Yb dxdy ,
n l = 1 n u .
d P s m d z = P s m ( σ s e n u σ s a n l ) N Yb Φ m dxdy ,

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