Abstract

We report on a polarimetry of harmonic mode-locked erbium-doped fiber laser with carbon nanotubes saturable absorber. We find new types of vector solitons with locked, switching and precessing states of polarization. The underlying physics presents interplay between birefringence of a laser cavity created by polarization controller along with light induced anisotropy caused by polarization hole burning.

© 2014 Optical Society of America

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  1. S. Arahira, H. Takahashi, K. Nakamura, H. Yaegashi, and Y. Ogawa, “Polarization-, wavelength-, and filter free all-optical clock recovery in a passively mode-locked laser diode with orthogonally pumped polarization diversity configuration,” IEEE J. Quantum Electron. 45, 476–487 (2009).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  15. L. M. Tong, V. D. Miljkovic, and M. Kall, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano. Lett. 10, 268–273 (2010).
    [CrossRef]
  16. N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
    [CrossRef]
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    [CrossRef]
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  19. L. Yun, X. Liu, and D. Mao, “Observation of dual-wavelength dissipative solitons in a figure-eight erbium-doped fiber laser,” Opt. Express 20(19), 20992–20997 (2012).
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  20. H. Zhang, D. Y. Tang, X. Wu, and L. M. Zhao, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser,” Opt. Express 17, 12692–12697 (2009).
    [CrossRef] [PubMed]
  21. N. Akhmediev and J. M. Soto-Crespo, “Dynamics of soliton-like pulse-propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
    [CrossRef]
  22. L. M. Zhao, D. Y. Tang, T. H. Cheng, C. Lu, H. Y. Tam, X. Q. Fu, and S. C. Wen, “Passive harmonic mode locking of soliton bunches in a fiber ring laser,” Optical and Quantum Electronics 40(13), 1053–1064 (2009).
    [CrossRef]

2014 (1)

S. Sergeyev, Ch. Mou, E. Turitsyna, A. Rozhin, S. K. Turitsyn, and K. Blow, “Spiral attractor created by vector solitons,” Light: Science & Applications 3, e131 (2014).

2013 (2)

V. Tsatourian, S. V. Sergeyev, Ch. Mou, S. K. Turitsyn, A. Rozhin, V. Mikhailov, P. Westbrook, and B. Rabin, “Polarisation dynamics of vector soliton molecules in mode locked fibre laser,” Sci. Rep. 3, 3154 (2013). doi:.
[CrossRef]

M. S. Kang, N. Y. Joly, and P. St. J. Russell, “Passive mode-locking of fiber ring laser at the 337th harmonic using gigahertz acoustic core resonances,” Opt. Lett. 38, 561–563 (2013).
[CrossRef] [PubMed]

2012 (3)

2011 (4)

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[CrossRef] [PubMed]

N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
[CrossRef]

F. Li, E. Ding, J. N. Kutz, and P. K. A. Wai, “Dual transmission filters for enhanced energy in mode-locked fiber lasers,” / Opt. Express 19, 23408–23419 (2011).
[CrossRef] [PubMed]

2010 (1)

L. M. Tong, V. D. Miljkovic, and M. Kall, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano. Lett. 10, 268–273 (2010).
[CrossRef]

2009 (4)

J. Mandon, G. Guelachvili, and N. Picque, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3, 99–102 (2009).
[CrossRef]

L. M. Zhao, D. Y. Tang, T. H. Cheng, C. Lu, H. Y. Tam, X. Q. Fu, and S. C. Wen, “Passive harmonic mode locking of soliton bunches in a fiber ring laser,” Optical and Quantum Electronics 40(13), 1053–1064 (2009).
[CrossRef]

S. Arahira, H. Takahashi, K. Nakamura, H. Yaegashi, and Y. Ogawa, “Polarization-, wavelength-, and filter free all-optical clock recovery in a passively mode-locked laser diode with orthogonally pumped polarization diversity configuration,” IEEE J. Quantum Electron. 45, 476–487 (2009).
[CrossRef]

H. Zhang, D. Y. Tang, X. Wu, and L. M. Zhao, “Multi-wavelength dissipative soliton operation of an erbium-doped fiber laser,” Opt. Express 17, 12692–12697 (2009).
[CrossRef] [PubMed]

2007 (1)

2006 (1)

D. Panasenko, P. Polynkin, A. Polynkin, J. V. Moloney, M. Mansuripur, and N. Peyghambarian, “Er-Yb Femtosecond ring fiber oscillator with 1.1-W average power and GHz repetition rates,” IEEE Photon. Technol. Lett. 18, 853–855 (2006).
[CrossRef]

2002 (2)

G. D. VanWiggeren and R. Roy, “Communication with dynamically fluctuating states of light polarization,” Phys. Rev. Lett. 88, 097903 (2002).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[CrossRef] [PubMed]

1997 (1)

1994 (1)

N. Akhmediev and J. M. Soto-Crespo, “Dynamics of soliton-like pulse-propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

1992 (1)

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Akhmediev, N.

N. Akhmediev and J. M. Soto-Crespo, “Dynamics of soliton-like pulse-propagation in birefringent optical fibers,” Phys. Rev. E 49, 5742–5754 (1994).
[CrossRef]

Arahira, S.

S. Arahira, H. Takahashi, K. Nakamura, H. Yaegashi, and Y. Ogawa, “Polarization-, wavelength-, and filter free all-optical clock recovery in a passively mode-locked laser diode with orthogonally pumped polarization diversity configuration,” IEEE J. Quantum Electron. 45, 476–487 (2009).
[CrossRef]

Arif, R.

C. Mou, R. Arif, A. Rozhin, and S. Turitsyn, “Passively harmonic mode locked erbium doped fiber soliton laser with carbon nanotubes based saturable absorber,” Opt. Mat. Express 2, 884–890 (2012).
[CrossRef]

Becker, J.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Ben Ezra, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Blow, K.

S. Sergeyev, Ch. Mou, E. Turitsyna, A. Rozhin, S. K. Turitsyn, and K. Blow, “Spiral attractor created by vector solitons,” Light: Science & Applications 3, e131 (2014).

Bonk, R.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Cheng, T. H.

L. M. Zhao, D. Y. Tang, T. H. Cheng, C. Lu, H. Y. Tam, X. Q. Fu, and S. C. Wen, “Passive harmonic mode locking of soliton bunches in a fiber ring laser,” Optical and Quantum Electronics 40(13), 1053–1064 (2009).
[CrossRef]

Diddams, S. A.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[CrossRef] [PubMed]

Ding, E.

Dreschmann, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Ellermeyer, T.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Freude, W.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Frey, F.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Fu, X. Q.

L. M. Zhao, D. Y. Tang, T. H. Cheng, C. Lu, H. Y. Tam, X. Q. Fu, and S. C. Wen, “Passive harmonic mode locking of soliton bunches in a fiber ring laser,” Optical and Quantum Electronics 40(13), 1053–1064 (2009).
[CrossRef]

Gray, S.

Grudinin, A. B.

Guelachvili, G.

J. Mandon, G. Guelachvili, and N. Picque, “Fourier transform spectroscopy with a laser frequency comb,” Nat. Photonics 3, 99–102 (2009).
[CrossRef]

Hansch, T. W.

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[CrossRef] [PubMed]

Higuchi, T.

N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
[CrossRef]

Hillerkuss, D.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Hoh, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Holzwarth, R.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[CrossRef] [PubMed]

T. Udem, R. Holzwarth, and T. W. Hansch, “Optical frequency metrology,” Nature 416, 233–237 (2002).
[CrossRef] [PubMed]

Huber, G.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Huebner, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Joly, N. Y.

Jordan, M.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Kall, M.

L. M. Tong, V. D. Miljkovic, and M. Kall, “Alignment, rotation, and spinning of single plasmonic nanoparticles and nanowires using polarization dependent optical forces,” Nano. Lett. 10, 268–273 (2010).
[CrossRef]

Kanda, N.

N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
[CrossRef]

Kang, M. S.

Kelly, S. M. J.

S. M. J. Kelly, “Characteristic sideband instability of periodically amplified average soliton,” Electron. Lett. 28, 806–807 (1992).
[CrossRef]

Kippenberg, T. J.

T. J. Kippenberg, R. Holzwarth, and S. A. Diddams, “Microresonator-based optical frequency combs,” Science 332, 555–559 (2011).
[CrossRef] [PubMed]

Kleinow, P.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Koenig, S.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Konishi, K.

N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
[CrossRef]

Koos, C.

D. Hillerkuss, R. Schmogrow, T. Schellinger, M. Jordan, M. Winter, G. Huber, T. Vallaitis, R. Bonk, P. Kleinow, F. Frey, M. Roeger, S. Koenig, A. Ludwig, A. Marculescu, J. Li, M. Hoh, M. Dreschmann, J. Meyer, S. Ben Ezra, N. Narkiss, B. Nebendahl, F. Parmigiani, P. Petropoulos, B. Resan, A. Oehler, K. Weingarten, T. Ellermeyer, J. Lutz, M. Moeller, M. Huebner, J. Becker, C. Koos, W. Freude, and J. Leuthold, “26 Tbit s(-1) 21 line-rate super-channel transmission utilizing all-optical fast Fourier transform processing,” Nature Photon. 5, 364–371 (2011).
[CrossRef]

Kutz, J. N.

Kuwata-Gonokami, M.

N. Kanda, T. Higuchi, H. Shimizu, K. Konishi, K. Yoshioka, and M. Kuwata-Gonokami, “The vectorial control of magnetization by light,” Nature Commun. 2, 1–5 (2011).
[CrossRef]

Leuthold, J.

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S. Sergeyev, Ch. Mou, E. Turitsyna, A. Rozhin, S. K. Turitsyn, and K. Blow, “Spiral attractor created by vector solitons,” Light: Science & Applications 3, e131 (2014).

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Figures (5)

Fig. 1
Fig. 1

Configuration of Erbium doped fiber laser with single wall carbon nanotubes (CNTs) saturable absorber. LD: laser diode, PC: polarization controller, WDM: wavelength division multiplexing coupler.

Fig. 2
Fig. 2

Polarization-locked vector solitons at (a1–f1) 4th harmonic (pump power 133 mW), and (a2–f2) 10th harmonics (pump power 162 mW). (a) Optical spectra, (b) pulse trains, (c) RF spectra, (d) normalized Stocks parameters, s1 (red), s2 (blue), s3 (green), (e) degrees of polarization (black) and output powers (red), (f) Poincaré spheres.

Fig. 3
Fig. 3

Combination of vector solitons at the fundamental and 3rd harmonic with slowly evolving polarization. (a) optical spectrum, (b) pulse train, (c) RF spectrum, (d) normalized Stocks parameters, s1 (red), s2 (blue), s3 (green), (e) degree of polarization (black) and output power (red), (d) Poincaré sphere. Pump power 147 mW.

Fig. 4
Fig. 4

Solitons group with switching polarization. (a) optical spectrum, (b) normalized Stocks parameters, (c) Poincaré sphere, (d) degree of polarization (black) and output power (red). Pump power 170 mW.

Fig. 5
Fig. 5

Vector solitons at 11th harmonic with (d) stable, (e) precessing in microsecond scale, and (f) chaotic polarization. (a) Optical spectra, (b) pulse trains, (c) RF spectra for stable (black), precessing (red), and chaotic (blue) polarization, (d–e) Poincaré spheres.

Equations (4)

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S 0 = | u | 2 + | ν | 2 ; S 1 = | u | 2 | ν | 2 ; S 2 = 2 | u | | ν | cos ( Δ ϕ ) ; S 3 = 2 | u | | ν | sin ( Δ ϕ ) .
s 1 , 2 , 3 = S 1 , 2 , 3 S 1 2 + S 2 2 + S 3 2 ; DOP = S 1 2 + S 2 2 + S 3 2 S 0 .
σ a , p = σ a ( p ) ( cos 2 ( θ ) + δ 2 sin 2 ( θ ) ) / ( 1 + δ 2 ) ,
h ( θ ) ~ | u | 2 cos 2 ( θ ) + | ν | 2 sin 2 ( θ ) + 2 | u | | ν | cos ( Δ ϕ ) cos ( θ ) sin ( θ ) ) .

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