Abstract

As fiber amplifiers and lasers achieve higher power, gain fiber designs are pushing toward extremely large-mode area. In this regime, bend-induced distortion of fiber modes becomes large and can severely impact amplifier performance. Previous results describing bend-induced reduction of effective area are reviewed and extended with a numerical analysis of how bend distortion impacts interaction with the gain. Distortion-resistant designs such as the parabolic fiber are shown to substantially improve gain-interaction indicators as well as all other performance metrics simulated, and are predicted to dramatically outperform step-index fibers.

© 2007 Optical Society of America

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2007 (1)

2006 (6)

2005 (5)

2004 (2)

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic-crystal-fiber-based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

S. Guo, F. Wu, S. Albin, H. Tai, and R. S. Rogowski, "Loss and dispersion analysis of microstructured fibers by finite-difference method," Opt. Express 12, 3341-3352 (2004).
[CrossRef] [PubMed]

2003 (2)

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

C. J. S. de Matos, J. R. Taylor, T. P. Hansen, K. P. Hansen, and J. Broeng, "All-fiber chirped pulse amplification using highly-dispersive air-core photonic bandgap fiber," Opt. Express 11, 2832-2837 (2003).
[CrossRef] [PubMed]

2002 (1)

2001 (3)

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, and D. J. Richardson, "Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding," Opt. Express 9, 714-720 (2001).
[CrossRef] [PubMed]

A. Galvanauskas, "Mode-scalable fiber-based chirped pulse amplification systems," IEEE J. Sel. Top. Quantum Electron. 7, 504-517 (2001).
[CrossRef]

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

2000 (1)

1998 (1)

1997 (2)

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

J. Nilsson, R. Paschotta, J. E. Caplen, and D. C. Hanna, "Yb3+-ring-doped fiber for high-energy pulse amplification," Opt. Lett. 22, 1092-1094 (1997).
[CrossRef] [PubMed]

1991 (1)

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

1990 (1)

E. Desurvire, J. L. Zyskind, and C. R. Giles, "Design optimization for efficient erbium-doped fiber amplifiers," J. Lightwave Technol. 8, 1730-1741 (1990).
[CrossRef]

1982 (1)

Albin, S.

Alvarez-Chavez, J. A.

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

Amezcua, R.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Andrejco, M. J.

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, "Increased pulsed amplifier efficiency by manipulating the fiber dopant distribution," in Conference on Lasers and Electro-optics (Optical Society of America, 2006), paper CTuQ3.

Baggett, J.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Baggett, J. C.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

Broderick, N.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Broeng, J.

Caplen, J. E.

Chang, Y.-C.

Changkakoti, R.

Chann, B.

Chen, X.

Cheng, M.-Y.

Clarkson, W. A.

P. Wang, L. J. Cooper, J. K. Sahu, and W. A. Clarkson, "Efficient single-mode operation of a cladding-pumped ytterbium-doped helical-core fiber laser," Opt. Lett. 31, 226-228 (2006).
[CrossRef] [PubMed]

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

Cooper, L. J.

Crowley, A.

Cucinotta, A.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic-crystal-fiber-based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

de Matos, C. J. S.

Deguil-Robin, N.

Desurvire, E.

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

E. Desurvire, J. L. Zyskind, and C. R. Giles, "Design optimization for efficient erbium-doped fiber amplifiers," J. Lightwave Technol. 8, 1730-1741 (1990).
[CrossRef]

DiGiovanni, D. J.

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, "Increased pulsed amplifier efficiency by manipulating the fiber dopant distribution," in Conference on Lasers and Electro-optics (Optical Society of America, 2006), paper CTuQ3.

Dimarcello, F.

Dong, L.

Farrow, R. L.

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, "Peak-power limits on fiber amplifiers imposed by self-focusing," Opt. Lett. 31, 3423-3425 (2006).
[CrossRef] [PubMed]

G. R. Hadley, R. L. Farrow, and A. V. Smith, "Bent-waveguide modeling of large-mode-area, double-clad fibers for high-power lasers," in Fiber Lasers III: Technology, Systems, and Applications, Proc. SPIE 6102, 61021S (2006).

Fermann, M. E.

Finazzi, V.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Fini, J. M.

J. M. Fini and S. Ramachandran, "Natural bend-distortion immunity of higher-order-mode large-mode-area fibers," Opt. Lett. 32, 748-750 (2007).
[CrossRef] [PubMed]

J. M. Fini, "Bend-compensated design of large-mode-area fibers," Opt. Lett. 31, 1963-1965 (2006).
[CrossRef] [PubMed]

J. M. Fini, "Bend-resistant design of conventional and microstructure fibers with very large mode area," Opt. Express 14, 69-81 (2006).
[CrossRef] [PubMed]

J. M. Fini and S. Ramachandran, "Bend resistance of large-mode-area higher-order-mode fibers," in Lasers and Electro-Optics Society Summer Topical Meeting (IEEE, 2006), paper MC1.3.

J. M. Fini, "Intuitive modeling of bend-distortion in large-mode-area fibers," Opt. Lett. (to be published).

Furusawa, K.

Galvanauskas, A.

Gatchell, P.

Ghalmi, S.

Giles, C. R.

C. R. Giles and E. Desurvire, "Modeling erbium-doped fiber amplifiers," J. Lightwave Technol. 9, 271-283 (1991).
[CrossRef]

E. Desurvire, J. L. Zyskind, and C. R. Giles, "Design optimization for efficient erbium-doped fiber amplifiers," J. Lightwave Technol. 8, 1730-1741 (1990).
[CrossRef]

Goldberg, L.

Gopinath, J. T.

Gray, S.

Grudinin, A. B.

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

Guo, S.

Hadley, G. R.

R. L. Farrow, D. A. V. Kliner, G. R. Hadley, and A. V. Smith, "Peak-power limits on fiber amplifiers imposed by self-focusing," Opt. Lett. 31, 3423-3425 (2006).
[CrossRef] [PubMed]

G. R. Hadley, R. L. Farrow, and A. V. Smith, "Bent-waveguide modeling of large-mode-area, double-clad fibers for high-power lasers," in Fiber Lasers III: Technology, Systems, and Applications, Proc. SPIE 6102, 61021S (2006).

Hanna, D. C.

J. Nilsson, R. Paschotta, J. E. Caplen, and D. C. Hanna, "Yb3+-ring-doped fiber for high-energy pulse amplification," Opt. Lett. 22, 1092-1094 (1997).
[CrossRef] [PubMed]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

Hansen, K. P.

Hansen, T. P.

Hayes, J.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Headley, C.

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, "Increased pulsed amplifier efficiency by manipulating the fiber dopant distribution," in Conference on Lasers and Electro-optics (Optical Society of America, 2006), paper CTuQ3.

Huang, R. K.

Jakobsen, C.

Juodawlkis, P. W.

Kliner, D. A. V.

Koplow, J. P.

Li, M.

Liem, A.

Limpert, J.

Malinowski, A.

Mamidipudi, P.

Manek-Hönninger, I.

Marcuse, D.

McLaughlin, J. M.

Monberg, E.

Monro, T.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Monro, T. M.

Moore, S. W.

Nicholson, J.

Nilsson, J.

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, and D. J. Richardson, "Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding," Opt. Express 9, 714-720 (2001).
[CrossRef] [PubMed]

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

J. Nilsson, R. Paschotta, J. E. Caplen, and D. C. Hanna, "Yb3+-ring-doped fiber for high-energy pulse amplification," Opt. Lett. 22, 1092-1094 (1997).
[CrossRef] [PubMed]

Nolte, S.

O'Driscoll, E.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Offerhaus, H. L.

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

Oh, J. M.

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, "Increased pulsed amplifier efficiency by manipulating the fiber dopant distribution," in Conference on Lasers and Electro-optics (Optical Society of America, 2006), paper CTuQ3.

Paschotta, R.

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

J. Nilsson, R. Paschotta, J. E. Caplen, and D. C. Hanna, "Yb3+-ring-doped fiber for high-energy pulse amplification," Opt. Lett. 22, 1092-1094 (1997).
[CrossRef] [PubMed]

Peng, X.

Petersson, A.

Petrovich, M.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Plant, J. J.

Poletti, F.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Poli, F.

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic-crystal-fiber-based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

Price, J. H. V.

Proudley, G.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Prudenzano, F.

Ramachandran, S.

Renaud, C. C.

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

Richardson, D.

J. C. Baggett, T. M. Monro, K. Furusawa, V. Finazzi, and D. Richardson, "Understanding bending losses in holey optical fibers," Opt. Commun. 227, 317-335 (2003).
[CrossRef]

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Richardson, D. J.

C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

K. Furusawa, A. Malinowski, J. H. V. Price, T. M. Monro, J. K. Sahu, J. Nilsson, and D. J. Richardson, "Cladding pumped ytterbium-doped fiber laser with holey inner and outer cladding," Opt. Express 9, 714-720 (2001).
[CrossRef] [PubMed]

Ripin, D. J.

Rogowski, R. S.

Röser, F.

Ruffin, B.

Sahu, J. K.

Salin, F.

Salter, P.

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

Schreiber, T.

Selleri, S.

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[CrossRef] [PubMed]

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Taylor, J. R.

Teodoro, F. D.

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Appl. Opt. (1)

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C. C. Renaud, H. L. Offerhaus, J. A. Alvarez-Chavez, J. Nilsson, W. A. Clarkson, P. W. Turner, D. J. Richardson, and A. B. Grudinin, "Characteristics of Q-switched cladding-pumped ytterbium-doped fiber lasers with different high-energy fiber designs," IEEE J. Quantum Electron. 37, 199-206 (2001).
[CrossRef]

R. Paschotta, J. Nilsson, A. C. Tropper, and D. C. Hanna, "Ytterbium-doped fiber amplifiers," IEEE J. Quantum Electron. 33, 1049-1056 (1997).
[CrossRef]

IEEE J. Sel. Top. Quantum Electron. (1)

A. Galvanauskas, "Mode-scalable fiber-based chirped pulse amplification systems," IEEE J. Sel. Top. Quantum Electron. 7, 504-517 (2001).
[CrossRef]

IEEE Photon. Technol. Lett. (1)

A. Cucinotta, F. Poli, and S. Selleri, "Design of erbium-doped triangular photonic-crystal-fiber-based amplifiers," IEEE Photon. Technol. Lett. 16, 2027-2029 (2004).
[CrossRef]

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[CrossRef]

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[CrossRef]

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[CrossRef]

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J. M. Fini, "Bend-compensated design of large-mode-area fibers," Opt. Lett. 31, 1963-1965 (2006).
[CrossRef] [PubMed]

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[CrossRef] [PubMed]

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Other (5)

G. R. Hadley, R. L. Farrow, and A. V. Smith, "Bent-waveguide modeling of large-mode-area, double-clad fibers for high-power lasers," in Fiber Lasers III: Technology, Systems, and Applications, Proc. SPIE 6102, 61021S (2006).

J. M. Fini, "Intuitive modeling of bend-distortion in large-mode-area fibers," Opt. Lett. (to be published).

J. Baggett, M. Petrovich, J. Hayes, V. Finazzi, F. Poletti, R. Amezcua, N. Broderick, D. Richardson, T. Monro, P. Salter, G. Proudley, and E. O'Driscoll, "Microstructured fibers for high power applications," Nanophotonics for Communication: Materials and Devices II, Proc. SPIE 6017, 40-54 (2005).

J. M. Oh, C. Headley, M. J. Andrejco, A. D. Yablon, and D. J. DiGiovanni, "Increased pulsed amplifier efficiency by manipulating the fiber dopant distribution," in Conference on Lasers and Electro-optics (Optical Society of America, 2006), paper CTuQ3.

J. M. Fini and S. Ramachandran, "Bend resistance of large-mode-area higher-order-mode fibers," in Lasers and Electro-Optics Society Summer Topical Meeting (IEEE, 2006), paper MC1.3.

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Figures (15)

Fig. 1
Fig. 1

Bend-induced distortion as seen in calculated mode intensity profiles: (a) A 32 μ m core-diameter fiber with no bend and (b) a 9 cm radius bend; (c) a 110 μ m core-diameter fiber with no bend and (d) a 15 cm radius bend. Core boundaries are shown as dashed circles.

Fig. 2
Fig. 2

Comparison of fibers with moderately large and extremely large core diameter. Despite a 13-fold increase in core area and an extremely large theoretical straight-fiber area, the larger-core fiber gives only about double the effective area in realistic, spooled-fiber conditions (bend radius 15 cm or less).

Fig. 3
Fig. 3

Conformal mapping model of macrobending defines an effective index profile that incorporates geometrical path-length differences together with the material index profile. The bend perturbation is an index gradient n core R bend toward the outside of the bend.

Fig. 4
Fig. 4

Simple schematic (left) describes the onset of large bend distortion. The effective index (horizontal line) and fiber index profiles (straight and curved, shown solid and dashed) define a forbidden region of the core (shaded). Distortion curves (right) for well-confined SIFs reduce to a single universal curve when rescaled using the intuitive sensitivity parameter. The curves from Fig. 2 are repeated in the rescaled axes (circles and stars) along with several other SIF simulations (dots) with a variety of core sizes and contrasts.

Fig. 5
Fig. 5

Gain overlap (left) is the fraction of optical power in the gain medium (shaded area), and is the simplest indication of differential gain between modes. The “dark fraction” of a gain profile (right) is a complimentary indicator, defined as the fraction of gain that sees too little signal-mode intensity for effective energy extraction (threshold shown dashed).

Fig. 6
Fig. 6

Mode intensities for the 32 μ m design of Fig. 1 imply gain-interaction parameters as in Fig. 5. Intensity is integrated along the y direction to give 1D curves for the fundamental (bold) and two HOMs (solid), shown along with the gain profile (dashed). The dark fraction is very low for a straight fiber (left), but increases as bend distortion excludes the fundamental from part of the core (right, R bend = 9 cm ).

Fig. 7
Fig. 7

For the 32 μ m fiber, bend loss (left) is low for the fundamental and high for the HOMs for bends with an 9 cm radius, allowing for selective HOM stripping in a fiber spool. The dark fraction (right, solid) is very low, indicating good extraction of energy from the gain. Dashed curves compare alternative dark fraction thresholds (3.3% ×, and 0.3% +) to the default 1% intensity-peak threshold (solid). All three thresholds give low dark fraction for R bend 9 cm .

Fig. 8
Fig. 8

Bend-loss calculations (left) for the 110 μ m fiber show almost no selectivity between the fundamental (solid curves) and HOMs (dashed curves). The dark fraction (right) is high at essentially all bend radii, consistent with the large distortion visible in the mode images in Fig. 1. Details differ for dark thresholds at 3.3% (×), 1.0% (엯), and 0.3% (+) of the peak intensity, but the qualitative impact of bend distortion on energy extraction is similar.

Fig. 9
Fig. 9

Graded-index fibers are resistant to bend distortion. The material index gradient cancels the bend-induced index gradient, leading to a broad, flat index peak.

Fig. 10
Fig. 10

Performance improves as a bend-compensating index gradient is introduced. For fair comparison to the 110 μ m SIF, a family of index profiles (left) is defined with fixed 0.08 dB m bend loss and A eff = 1100 μ m 2 at R bend = 15 cm . Calculated losses (right) for fully graded profile show greatly improved HOM suppression (compare with Fig. 8).

Fig. 11
Fig. 11

Loss suppression (ratio of HOM to fundamental losses) and effective index difference (fundamental minus HOM) improve steadily as the depth of the graded index is increased (left). Dark fraction increases for tighter bends (right) but can be substantially improved by using graded-index designs.

Fig. 12
Fig. 12

SIF with 50 μ m core diameter and contrast Δ n core = 0.00058 achieves 800 μ m 2 mode area at R bend = 15 cm (left), and losses (right) for fundamental (solid) and HOMs comparable to the 1100 μ m 2 parabolic design.

Fig. 13
Fig. 13

Gain-dopant profile can be adjusted independently of the index profile to better match the desired signal mode or suppress the HOM gain (left, compare with Fig. 5). Simulated straight-fiber intensity versus radius curves are integrated to give gain overlap versus R gain , plotted together (right). With no bend, the fundamental gain overlap (solid curves) is greater than the HOM gain overlaps (selected modes shown as dashed curves) for a range of gain-dopant radii, indicating selective amplification of the fundamental mode over other modes.

Fig. 14
Fig. 14

In the large-core SIF (left) large bend distortion makes preferential gain impossible. The signal mode intensity (solid) now lies farther out than the HOMs (dashed). The distortion-resistant graded-index design enables preferential gain, with fundamental overlap (solid curves) greater than HOM overlap (dashed curves).

Fig. 15
Fig. 15

For the graded-index designs, differential gain can provide significant HOM suppression if the dopant radius R gain is chosen carefully. The gain overlap ratio (left) at R bend = 15 cm indicates preferential gain of the fundamental for the graded-index fibers, and improves as the degree of gradation increases. The fully graded design ( Δ n grad Δ n grad ) with a confined dopant R gain 22 μ m simultaneously achieves low dark fraction (right, circles) and high gain overlap (squares) for the target range of bend radii.

Equations (12)

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Δ n bend = n core R core R bend ,
Δ n eff = n core n eff .
Δ n bend Δ n eff = S R bend ,
S n core R core Δ n eff .
R bend > S R core 3 .
g k ( z ) = σ e k n 2 ( r , θ , z ) i k ( r , θ , z ) d A ,
d d t n 2 ( r , θ , z ) = n 2 τ + k I k h ν k ( σ a k n 1 σ e k n 2 ) .
g k = g 0 r < R gain I k d A I k d A = g 0 Γ k .
d n 2 d t I s n 2 ( σ a s + σ e s ) h ν k ,
I s * τ pulse = h ν k ( σ a s + σ e s ) = U sat .
I s * I s , peak = U sat A s P s τ pulse ,
I s * I s , peak = ( E sat E s ) ( Γ s A s A doped ) .

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