Abstract

We model the transverse mode interaction in a large-mode-area fiber amplifier by solving the Fresnel wave equation including local gain saturation. In order to calculate the electric field distribution we apply a finite difference beam propagation method, which is followed by the derivation of the modal powers and modal polarization states. A polarization dependent mode amplification is found that is in good agreement with recent experimental results.

© 2008 Optical Society of America

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References

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  1. Y. Jeong, J. Nilsson, J. K. Sahu, D. B. Soh, P. Dupriez, C. A. Codemard, S. Baek, D. N. Payne, R. Horley, J. A. Alvarez-Chavez, and P. W. Turner, "Single-mode plane-polarized ytterbium-doped large-core fiber laser with 633-W continuous-wave output power," Opt. Lett. 30, 955-957 (2005).
    [CrossRef] [PubMed]
  2. Y. Jeong, J. Nilsson, J. K. Sahu, D. B. S. Soh, C. Alegria, P. Dupriez, C. A. Codemard, D. N. Payne, R. Horley, L. M. B. Hickey, L. Wanzcyk, C. E. Chryssou, J. A. Alvarez-Chavez, and P. W. Turner, "Single-frequency, singlemode, plane-polarized ytterbium-doped fiber master oscillator power amplifier source with 264 W of output power," Opt. Lett. 30, 459-461 (2005).
    [CrossRef] [PubMed]
  3. P. Weßels and C. Fallnich, "Highly sensitive beam quality measurements on large-mode-area fiber amplifiers," Opt. Express 11, 3346-3351 (2003).
  4. A. Galvanauskas, M. C. Swan, and C.-H. Liu, "Effectively-single-mode large core passive and active fibers with chirally-coupled-core structures," presented at the Conference on Lasers and Electro-Optics, San Jose, USA, 4-9 May 2008.
  5. L. Dong, J. Li, and X. Peng, "Bend-resistant fundamental mode operation in ytterbium-doped leakage channel fibers with effective areas up to 3160μm2," Opt. Express 14, 11512-11519 (2006).
    [CrossRef] [PubMed]
  6. O. Schmidt, J. Rothhardt, T. Eidam, F. R¨oser, J. Limpert, A. T¨unnermann, K. P. Hansen, C. Jakobsen, and J. Broeng, "Single-polarization ultra-large-mode-area Yb-doped photonic crystal fiber," Opt. Express 16, 3918-3923 (2008).
    [CrossRef] [PubMed]
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    [CrossRef]
  8. S. Ramachandran, J. W. Nicholson, S. Ghalmi, M. F. Yan, P. Wisk, E. Monberg, and F. V. Dimarcello, "Light propagation with ultralarge modal areas in optical fibers," Opt. Lett. 31, 1797-1799 (2006).
    [CrossRef] [PubMed]
  9. G. Nemova and R. Kashyap, "High-power long-period-grating-assisted erbium-doped fiber amplifier," J. Opt. Soc. Am. B 25, 1322-1327 (2008).
    [CrossRef]
  10. A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 1983).
  11. J. M. Fini, "Bend-compensated design of large-mode-area fibers," Opt. Lett. 31, 1963-1965 (2006).
    [CrossRef] [PubMed]
  12. D. Yevick, "A guide to electric field propagation techniques for guided-wave optics," Opt. Quantum Electron. 26, 185-197 (1994).
    [CrossRef]
  13. 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).
    [CrossRef] [PubMed]
  14. 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, 1539-1543 (2002).
    [CrossRef]
  15. M. Gong, Y. Yuan, C. Li, P. Yan, H. Zhang, and S. Liao, "Numerical modeling of transverse mode competition in strongly pumped multimode fiber lasers and amplifiers," Opt. Express 15, 3236-3246 (2007).
    [CrossRef] [PubMed]
  16. Z. Jiang and J. R. Marciante, "Impact of transverse spatial-hole burning on beam quality in large-mode-area Yb-doped fibers," J. Opt. Soc. Am. B 25, 247-254 (2008).
    [CrossRef]
  17. N. Andermahr, T. Theeg, and C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).
    [CrossRef]

2008 (5)

2007 (2)

2006 (3)

2005 (2)

2003 (1)

2002 (1)

1994 (1)

D. Yevick, "A guide to electric field propagation techniques for guided-wave optics," Opt. Quantum Electron. 26, 185-197 (1994).
[CrossRef]

Alegria, C.

Alvarez-Chavez, J. A.

Andermahr, N.

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).
[CrossRef] [PubMed]

N. Andermahr, T. Theeg, and C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).
[CrossRef]

Baek, S.

Beach, R. J.

Bhutta, T.

Broeng, J.

Chryssou, C. E.

Codemard, C. A.

Dimarcello, F. V.

Dong, L.

Dupriez, P.

Eidam, T.

Fallnich, C.

Fini, J. M.

Ghalmi, S.

Gong, M.

Hansen, K. P.

Hickey, L. M. B.

Horley, R.

Jakobsen, C.

Jeong, Y.

Jiang, Z.

Kashyap, R.

Li, C.

Li, J.

Liao, S.

Limpert, J.

Mackenzie, J. I.

Marciante, J. R.

Monberg, E.

Nemova, G.

Nicholson, J. W.

Nilsson, J.

Payne, D. N.

Peng, X.

R¨oser, F.

Ramachandran, S.

Rothhardt, J.

Sahu, J. K.

Schmidt, O.

Shepherd, D. P.

Siegman, A. E.

Soh, D. B.

Soh, D. B. S.

T¨unnermann, A.

Theeg, T.

N. Andermahr, T. Theeg, and C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).
[CrossRef]

Turner, P. W.

Wanzcyk, L.

Weßels, P.

Wisk, P.

Yan, M. F.

Yan, P.

Yevick, D.

D. Yevick, "A guide to electric field propagation techniques for guided-wave optics," Opt. Quantum Electron. 26, 185-197 (1994).
[CrossRef]

Yuan, Y.

Zhang, H.

Appl. Phys. B (1)

N. Andermahr, T. Theeg, and C. Fallnich, "Novel approach for polarization-sensitive measurements of transverse modes in few-mode optical fibers," Appl. Phys. B 91, 353-357 (2008).
[CrossRef]

J. Opt. Soc. Am. B (4)

Opt. Express (5)

Opt. Lett. (4)

Opt. Quantum Electron. (1)

D. Yevick, "A guide to electric field propagation techniques for guided-wave optics," Opt. Quantum Electron. 26, 185-197 (1994).
[CrossRef]

Other (2)

A. W. Snyder and J. D. Love, Optical Waveguide Theory (Kluwer Academic Publishers, 1983).

A. Galvanauskas, M. C. Swan, and C.-H. Liu, "Effectively-single-mode large core passive and active fibers with chirally-coupled-core structures," presented at the Conference on Lasers and Electro-Optics, San Jose, USA, 4-9 May 2008.

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Figures (6)

Fig. 1.
Fig. 1.

Analytically calculated electric field of 2D transverse modes: (a) fundamental mode, (b) first higher-order mode.

Fig. 2.
Fig. 2.

Propagation of two modes: (a) gain (shown in linear scale) over propagation distance, (b) intensity distribution within the fiber (normalized for each slice), (c) relative modal powers in modes for p- and s- polarizations, (d) modal polarizations illustrated on the Poincaré sphere (the circles correspond to the initial conditions).

Fig. 3.
Fig. 3.

The spherical distance as a measure for the difference of the modal polarizations: (a) simulation data, (b) experimental data from [13]. (The gain is shown in linear scale.)

Fig. 4.
Fig. 4.

The intensity distribution: (a–c) of the modes LP 01, LP 11 and LP 1′1, (d) of the superposition of the modes used as initial condition, and (e) after amplification in the fiber.

Fig. 5.
Fig. 5.

Propagation of three modes: (a) modal powers, (b) modal polarization states illustrated on the Poincaré sphere (the circles correspond to the initial conditions). (The gain is shown in linear scale.)

Fig. 6.
Fig. 6.

For the case that three modes propagate we calculated the spherical distances between: LP 01 and LP 11 (d 1), LP 01 and LP 1′1 (d 2), LP 11 and LP 11 (d 3), and the sum of all distances (d 4=d 1+d 2+d 3). Figure (a) shows simulation data and (b) experimental data (see [13] for measurement details). (The gain is shown in linear scale.)

Tables (1)

Tables Icon

Table 1. Modeling parameters used for the 2D- and the 3D-simulations.

Equations (8)

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2 E ( r ) + k 2 ( r ) E ( r ) = 0 ,
k ( r ) = n ( r ) k 0 i α ( r , I ( r ) ) 2 ,
α ( r ) = α ss ( r ) 1 + I ( r ) I sat .
2 i k av · A ( r ) z + t 2 A ( r ) + ( k 2 ( r ) k av 2 ) A ( r ) = 0 ,
c i ( z ) = c ε 0 n 2 + A ( r t , z ) E i ( r t ) d r t .
A = ( A p A s ) , c i = ( c i , p c i , s ) .
α i = α ( r t ) I i ( r t ) d r t ,
A ( x , z = 0 ) = E 0 ( x ) · ( c 0 , p c 0 , s ) + E 1 ( x ) · ( c 1 , p c 1 , s ) .

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