Abstract

The saturable absorption characteristics of two-, three-, and five-core one-dimensional fiber coupler arrays and the seven-core hexagonal fiber coupler array are investigated. It is shown that the performance of all these saturable absorbers is comparable and not much is gained, if anything, by going from a two-core nonlinear coupler geometry to a higher number of cores. This observation is supported by the similarity of the saturable absorption curves, as well as comparable pulse characteristics obtained from the simulation of a generic mode-locked fiber laser cavity.

© 2013 Optical Society of America

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    [CrossRef]
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2013 (2)

2012 (2)

2010 (1)

2009 (2)

B. Ortac, M. Baumgartl, J. Limpert, and A. Tunnermann, “Approaching microjoule-level pulse energy with mode-locked femtosecond fiber lasers,” Opt. Lett. 34, 1585–1587 (2009).
[CrossRef]

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

2008 (2)

Y. W. Song, S. Yamashita, and S. Maruyama, “Single-walled carbon nanotubes for high-energy optical pulse formation,” Appl. Phys. Lett. 92, 021115 (2008).
[CrossRef]

D. D. Hudson, K. Shish, T. R. Schibli, J. N. Kutz, D. N. Christodoulides, R. Morandotti, and S. T. Cundiff, “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33, 1440–1442 (2008).
[CrossRef]

2006 (1)

2005 (2)

2004 (2)

S. Y. Set, H. Yaguchi, Y. Tanaka, and M. Jablonski, “Laser mode locking using a saturable absorber incorporating carbon nanotubes,” J. Lightwave Technol. 22, 51–56 (2004).
[CrossRef]

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[CrossRef]

2000 (3)

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

G. Lenz, J. Zimmermann, T. Katsufuji, M. E. Lines, H. Y. Hwang, S. Spälter, R. E. Slusher, S.-W. Cheong, J. S. Sanghera, and I. D. Aggarwal, “Large Kerr effect in bulk Se-based chalcogenide glasses,” Opt. Lett. 25, 254–256 (2000).
[CrossRef]

1999 (1)

1998 (1)

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

1996 (1)

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

1992 (2)

D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation,” Electron. Lett. 28, 2185–2186 (1992).
[CrossRef]

H. G. Winful and D. T. Walton, “Passive mode locking through nonlinear coupling in a dual-core fiber laser,” Opt. Lett. 17, 1688–1690 (1992).
[CrossRef]

1991 (1)

1988 (2)

1982 (1)

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

1973 (1)

B. K. Garside and T. K. Lim, “Laser mode locking using saturable absorbers,” J. Appl. Phys. 44, 2335–2342 (1973).
[CrossRef]

Aggarwal, I. D.

Agrawal, G. P.

G. P. Agrawal, Nonlinear Fiber Optics, 5th ed. (Elsevier, 2013).

Aitchison, J. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Aus der Au, J.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Baumgartl, M.

Betlej, A.

Bise, R. T.

Bonaccorso, F.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Boyd, A. R.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Braun, B.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Büttner, T. F. S.

Casas Bedoya, A.

Chao, Q.

Q. Chao, D. D. Hudson, J. N. Kutz, and S. T. Cundiff, “Waveguide array fiber laser,” IEEE Photon. J. 4, 1438–1442 (2012).
[CrossRef]

Cheong, S.-W.

Christodoulides, D. N.

Cundiff, S. T.

Deng, Y.

DiGiovanni, D. J.

Eggleton, B. J.

Eisenberg, H. S.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Erhard, S.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Ferrari, A. C.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Fini, J.

Fluck, R.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Friberg, S. R.

Fujiwara, S.

Galvanauskas, A.

Garside, B. K.

B. K. Garside and T. K. Lim, “Laser mode locking using saturable absorbers,” J. Appl. Phys. 44, 2335–2342 (1973).
[CrossRef]

Giesen, A.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Grange, R.

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[CrossRef]

Haiml, M.

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[CrossRef]

Hasan, T.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Haus, H. A.

H. A. Haus, “Mode-locking of lasers,” IEEE J. Sel. Top. Quantum Electron. 6, 1173–1185 (2000).
[CrossRef]

Hirao, K.

Honninger, C.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Hövel, R.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Hudson, D. D.

Hwang, H. Y.

Jablonski, M.

Jankovic, L.

Jensen, S. M.

S. M. Jensen, “The nonlinear coherent coupler,” IEEE J. Quantum Electron. 18, 1580–1583 (1982).
[CrossRef]

Joseph, R. I.

Jung, I. D.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Kafka, J. D.

Kanbara, H.

Karszewski, M.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Kartner, F. X.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Katsufuji, T.

Kean, P. N.

Keller, U.

M. Haiml, R. Grange, and U. Keller, “Optical characterization of semiconductor saturable absorbers,” Appl. Phys. B 79, 331–339 (2004).
[CrossRef]

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Kieu, K.

Kopf, D.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Kutz, J. N.

Lefrancois, S.

Lenz, G.

Lim, T. K.

B. K. Garside and T. K. Lim, “Laser mode locking using saturable absorbers,” J. Appl. Phys. 44, 2335–2342 (1973).
[CrossRef]

Limpert, J.

Lines, M. E.

Liu, C.-H.

Mafi, A.

Mägi, E. C.

Makris, K. G.

Maruyama, S.

Y. W. Song, S. Yamashita, and S. Maruyama, “Single-walled carbon nanotubes for high-energy optical pulse formation,” Appl. Phys. Lett. 92, 021115 (2008).
[CrossRef]

Matuschek, N.

U. Keller, K. J. Weingarten, F. X. Kartner, D. Kopf, B. Braun, I. D. Jung, R. Fluck, C. Honninger, N. Matuschek, and J. Aus der Au, “Semiconductor saturable absorber mirrors (SESAM’s) for femtosecond to nanosecond pulse generation in solid-state lasers,” IEEE J. Sel. Top. Quantum Electron. 2, 435–453 (1996).
[CrossRef]

Morandotti, R.

D. D. Hudson, K. Shish, T. R. Schibli, J. N. Kutz, D. N. Christodoulides, R. Morandotti, and S. T. Cundiff, “Nonlinear femtosecond pulse reshaping in waveguide arrays,” Opt. Lett. 33, 1440–1442 (2008).
[CrossRef]

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

Morier-Genoud, F.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Moser, M.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Nazemosadat, E.

Noske, D. U.

D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation,” Electron. Lett. 28, 2185–2186 (1992).
[CrossRef]

Ortac, B.

Pandit, N.

D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation,” Electron. Lett. 28, 2185–2186 (1992).
[CrossRef]

Paschotta, R.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Proctor, J. L.

Rozhin, A. G.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Saleh, B. E. A.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Sanghera, J. S.

Schibli, T. R.

Set, S. Y.

Sfez, B. G.

Shimizugawa, Y.

Shish, K.

Sibbett, W.

Silberberg, Y.

H. S. Eisenberg, Y. Silberberg, R. Morandotti, A. R. Boyd, and J. S. Aitchison, “Discrete spatial optical solitons in waveguide arrays,” Phys. Rev. Lett. 81, 3383–3386 (1998).
[CrossRef]

S. R. Friberg, A. M. Weiner, Y. Silberberg, B. G. Sfez, and P. S. Smith, “Femotosecond switching in a dual-core-fiber nonlinear coupler,” Opt. Lett. 13, 904–906 (1988).
[CrossRef]

Slusher, R. E.

Smith, P. S.

Song, Y. W.

Y. W. Song, S. Yamashita, and S. Maruyama, “Single-walled carbon nanotubes for high-energy optical pulse formation,” Appl. Phys. Lett. 92, 021115 (2008).
[CrossRef]

Sosnowski, T. S.

Spälter, S.

Spence, D. E.

Spühler, G. J.

R. Paschotta, J. Aus der Au, G. J. Spühler, F. Morier-Genoud, R. Hövel, M. Moser, S. Erhard, M. Karszewski, A. Giesen, and U. Keller, “Diode-pumped passively mode-locked lasers with high average power,” Appl. Phys. B 70, S25–S31 (2000).
[CrossRef]

Stegeman, G. I.

Stock, M. L.

Sugimoto, N.

Sun, Z.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Suntsov, S.

Tan, P. H.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Tanaka, K.

Tanaka, Y.

Taunay, T.

Taylor, J. R.

D. U. Noske, N. Pandit, and J. R. Taylor, “Subpicosecond soliton pulse formation from self-mode-locked erbium fibre laser using intensity dependent polarisation rotation,” Electron. Lett. 28, 2185–2186 (1992).
[CrossRef]

Teich, M. C.

B. E. A. Saleh and M. C. Teich, Fundamentals of Photonics, 2nd ed. (Wiley, 2007).

Tunnermann, A.

Walton, D. T.

Wang, F.

T. Hasan, Z. Sun, F. Wang, F. Bonaccorso, P. H. Tan, A. G. Rozhin, and A. C. Ferrari, “Nanotube-polymer composites for ultrafast photonics,” Adv. Mater. 21, 3874–3899 (2009).
[CrossRef]

Weiner, A. M.

Weingarten, K. J.

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Figures (4)

Fig. 1.
Fig. 1.

Two-, three-, and five-core 1D arrays and the seven-core hexagonal array are shown in a fiber-optic geometry. All cores are assumed to be identical in a given geometry. The launch core is identified with a darker shade.

Fig. 2.
Fig. 2.

Transmission through the two-core (solid black), three-core (dashed red), and five-core (dotted orange) fiber 1D arrays and the seven-core hexagonal array (dashed–dotted purple) is shown as a function of the normalized length in the linear regime.

Fig. 3.
Fig. 3.

Nonlinear transmission through two-core (solid black), three-core (dashed red), five-core (dotted orange) fiber 1D arrays and the seven-core hexagonal array (dashed–dotted purple) is shown as a function of the normalized nonlinear strength γ˜, which is assumed to be the same for all cores. The length of each SA array is chosen to be equal to the half-beat length.

Fig. 4.
Fig. 4.

Normalized peak power of the mode-locked pulses is shown as a function of the length the SA, where the core-to-core coupling coefficients c are adjusted so that the length of the SA is equal to the half-beat length.

Equations (3)

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Enζ=in˜En˜+iγ˜n|En|2En+in˜μn,n˜|En˜|2En.
Az=αA+i22AT2+iη|A|2A+g(z)(1+τ2T2)A,
g(z)=2g01+A2/e0,

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