Abstract

An all-fiber tunable laser was fabricated based on an acousto-optic tunable filter and a tapered fiber. The structure was of a high signal-to-noise ratio, therefore, no extra gain flattening was needed in the laser. In the experiment, the wavelength of the laser could be tuned from 1532.1 nm to 1570.4 nm with a 3-dB bandwidth of about 0.2 nm. Given enough nonlinearity in the laser cavity, it could also generate a sliding-frequency pulse train. The laser gains advantages of fast tuning and agility in pulse generation, and its simple structure is low cost for practical applications.

© 2016 Optical Society of America

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References

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    [Crossref]
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    [Crossref]
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2015 (1)

2014 (3)

2013 (3)

2012 (1)

2010 (2)

2009 (1)

2008 (2)

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

S. Y. Li, N. Q. Ngo, and Z. R. Zhang, “Tunable fiber laser with ultra-narrow linewidth using a tunable phase-shifted chirped fiber grating,” IEEE Photonics Technol. Lett. 20, 1482–1484 (2008).
[Crossref]

2007 (2)

2005 (1)

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

2002 (1)

1998 (1)

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

1997 (1)

1996 (1)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

1995 (1)

1994 (3)

T. A. Birks, S. G. Farwell, P. S. J. Russell, and C. N. Pannell, “Four-port fiber frequency shifter with a null taper coupler,” Opt. Lett. 19, 1964–1966 (1994).
[Crossref] [PubMed]

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

1992 (2)

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

G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420–422 (1992).
[Crossref] [PubMed]

1990 (1)

1986 (1)

Al-Taiy, H.

Andrés, M. V.

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

Antonio-Lopez, J. E.

Ball, G. A.

Bhatia, V.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Birks, T. A.

Blake, J. N.

Bo, F.

Bossalini, L.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Canning, J.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Castillo-Guzman, A.

Chow, C. W.

Cook, K.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Cruz, J. L.

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

Culverhouse, D. O.

da Silva, R. E.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Delgado-Pinar, M.

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

Dennis, M. L.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

Díez, A.

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

Digonnet, M. J. F.

Duling, I. N.

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

Eiselt, M. H.

Elbers, J. P.

Engan, H. E.

Erdogan, T.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Estudillo-Ayala, J.

Farwell, S. G.

Feng, M.

Feng, X.

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

Fontana, F.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Franco, P.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Gao, F.

Gao, W.

Grobe, K.

Haakestad, M. W.

Huang, L. G.

Hwang, I. K.

Jain, R. K.

Jiang, B. Q.

Jiang, W. S.

Judkins, J. B.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Kelly, S. M. J.

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

Kim, B. Y.

Kim, H. K.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

Kim, H. S.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22, 1476–1478 (1997).
[Crossref]

Klinger, J.

Kwang, I. K.

Lee, K. J.

Lemaire, P. J.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Li, S. Y.

S. Y. Li, N. Q. Ngo, and Z. R. Zhang, “Tunable fiber laser with ultra-narrow linewidth using a tunable phase-shifted chirped fiber grating,” IEEE Photonics Technol. Lett. 20, 1482–1484 (2008).
[Crossref]

Libatique, N. J. C.

LikamWa, P.

Liu, X. M.

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

Liu, Y. G.

Liu, Z. B.

Mao, D.

Marques, C. A. F.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

May-Arrioja, D. A.

Miao, R.

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

Midrio, M.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Mora, J.

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

Morey, W. W.

Neves, P. d. T.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Ngo, N. Q.

S. Y. Li, N. Q. Ngo, and Z. R. Zhang, “Tunable fiber laser with ultra-narrow linewidth using a tunable phase-shifted chirped fiber grating,” IEEE Photonics Technol. Lett. 20, 1482–1484 (2008).
[Crossref]

Nogueira, R. N.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Oliveira, R. A.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Pachnicke, S.

Pannell, C. N.

Park, H. C.

Park, H. S.

Park, N.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

Pohl, A. A. P.

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Preußler, S.

Richardson, D. J.

Romagnoli, M.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Russell, P. S. J.

Schneider, T.

Selvas-Aguilar, R.

Shaw, H. J.

Sheng, Q. W.

Sipe, J. E.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Skaar, J.

Tian, J. G.

Tsang, H. K.

Tseng, F. G.

Vengsarkar, A. M.

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

Wabnitz, S.

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

Wang, L.

Wang, P.

Wenzel, N.

Wong, C. Y.

Wysocki, P. F.

Xin, W.

Xing, F.

Xu, J. J.

Xuan, L.

Yang, D. X.

Yang, L. G.

Yeh, C. H.

Yeom, D. I.

Yun, S. H.

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22, 1476–1478 (1997).
[Crossref]

Zhang, G. Q.

Zhang, W.

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

Zhang, W. D.

Zhang, Z. R.

S. Y. Li, N. Q. Ngo, and Z. R. Zhang, “Tunable fiber laser with ultra-narrow linewidth using a tunable phase-shifted chirped fiber grating,” IEEE Photonics Technol. Lett. 20, 1482–1484 (2008).
[Crossref]

Zhao, J. H.

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

Zhao, J. L.

Electron. Lett. (2)

F. Fontana, L. Bossalini, P. Franco, M. Midrio, M. Romagnoli, and S. Wabnitz, “Self-starting sliding-frequency fibre soliton laser,” Electron. Lett. 30, 321–322 (1994).
[Crossref]

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

IEEE J. Quantum Electron. (1)

M. L. Dennis and I. N. Duling, “Experimental study of sideband generation in femtosecond fiber lasers,” IEEE J. Quantum Electron. 30, 1469–1477 (1994).
[Crossref]

IEEE Photonics Technol. Lett. (3)

S. Y. Li, N. Q. Ngo, and Z. R. Zhang, “Tunable fiber laser with ultra-narrow linewidth using a tunable phase-shifted chirped fiber grating,” IEEE Photonics Technol. Lett. 20, 1482–1484 (2008).
[Crossref]

H. S. Kim, S. H. Yun, H. K. Kim, N. Park, and B. Y. Kim, “Actively gain-flattened erbium-doped fiber amplifier over 35nm by using all-fiber acoustooptic tunable filters,” IEEE Photonics Technol. Lett. 10, 790–792 (1998).
[Crossref]

M. Delgado-Pinar, J. Mora, A. Díez, J. L. Cruz, and M. V. Andrés, “Wavelength-switchable fiber laser using acoustic waves,” IEEE Photonics Technol. Lett. 17, 552–554 (2005).
[Crossref]

J. Lightwave Technol. (2)

A. M. Vengsarkar, P. J. Lemaire, J. B. Judkins, V. Bhatia, T. Erdogan, and J. E. Sipe, “Long-period fiber gratings as band-rejection filters,” J. Lightwave Technol. 14, 58–65 (1996).
[Crossref]

K. Grobe, M. H. Eiselt, S. Pachnicke, and J. P. Elbers, “Access networks based on tunable lasers,” J. Lightwave Technol. 32, 2815–2823 (2014).
[Crossref]

Opt. Express (10)

W. D. Zhang, W. Gao, L. G. Huang, D. Mao, B. Q. Jiang, F. Gao, D. X. Yang, G. Q. Zhang, J. J. Xu, and J. L. Zhao, “Optical heterodyne micro-vibration measurement based on all-fiber acousto-optic frequency shifter,” Opt. Express 23, 17576–17583 (2015).
[Crossref] [PubMed]

L. G. Yang, C. H. Yeh, C. Y. Wong, C. W. Chow, F. G. Tseng, and H. K. Tsang, “Stable and wavelength-tunable silicon-micro-ring-resonator based erbium-doped fiber laser,” Opt. Express 21, 2869–2874 (2013).
[Crossref] [PubMed]

W. D. Zhang, L. G. Huang, F. Gao, F. Bo, G. Q. Zhang, and J. J. Xu, “Tunable broadband light coupler based on two parallel all-fiber acousto-optic tunable filters,” Opt. Express 21, 16621–16628 (2013).
[Crossref] [PubMed]

W. Xin, Z. B. Liu, Q. W. Sheng, M. Feng, L. G. Huang, P. Wang, W. S. Jiang, F. Xing, Y. G. Liu, and J. G. Tian, “Flexible graphene saturable absorber on two-layer structure for tunable mode-locked soliton fiber laser,” Opt. Express 22, 10239–10247 (2014).
[Crossref] [PubMed]

N. J. C. Libatique, L. Wang, and R. K. Jain, “Single-longitudinal-mode tunable WDM-channel-selectable fiber laser,” Opt. Express 10, 1503–1507 (2002).
[Crossref] [PubMed]

K. J. Lee, D. I. Yeom, and B. Y. Kim, “Narrowband, polarization insensitive all-fiber acousto-optic tunable bandpass filter,” Opt. Express 15, 2987–2992 (2007).
[Crossref] [PubMed]

K. J. Lee, H. C. Park, H. S. Park, and B. Y. Kim, “Highly efficient all-fiber tunable polarization filter using torsional acoustic wave,” Opt. Express 15, 12362–12367 (2007).
[Crossref] [PubMed]

M. W. Haakestad and J. Skaar, “Slow and fast light in optical fibers using acoustooptic coupling between two co-propagating modes,” Opt. Express 17, 346–357 (2009).
[Crossref] [PubMed]

A. Castillo-Guzman, J. E. Antonio-Lopez, R. Selvas-Aguilar, D. A. May-Arrioja, J. Estudillo-Ayala, and P. LikamWa, “Widely tunable erbium-doped fiber laser based on multimode interference effect,” Opt. Express 18, 591–597 (2010).
[Crossref] [PubMed]

K. J. Lee, I. K. Hwang, H. C. Park, and B. Y. Kim, “Sidelobe suppression in all-fiber acousto-optic tunable filter using torsional acoustic wave,” Opt. Express 18, 12059–12064 (2010).
[Crossref] [PubMed]

Opt. Lett. (8)

W. D. Zhang, L. G. Huang, F. Gao, F. Bo, L. Xuan, G. Q. Zhang, and J. J. Xu, “Tunable add/drop channel coupler based on an acousto-optic tunable filter and a tapered fiber,” Opt. Lett. 37, 1241–1243 (2012).
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B. Y. Kim, J. N. Blake, H. E. Engan, and H. J. Shaw, “All-fiber acousto-optic frequency shifter,” Opt. Lett. 11, 389–391 (1986).
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P. F. Wysocki, M. J. F. Digonnet, and B. Y. Kim, “Electronically tunable, 1.55-μm erbium-doped fiber laser,” Opt. Lett. 15, 273–275 (1990).
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G. A. Ball and W. W. Morey, “Continuously tunable single-mode erbium fiber laser,” Opt. Lett. 17, 420–422 (1992).
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T. A. Birks, S. G. Farwell, P. S. J. Russell, and C. N. Pannell, “Four-port fiber frequency shifter with a null taper coupler,” Opt. Lett. 19, 1964–1966 (1994).
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D. O. Culverhouse, D. J. Richardson, T. A. Birks, and P. S. J. Russell, “All-fiber sliding-frequency Er3+/Yb3+ soliton laser,” Opt. Lett. 20, 2381–2383 (1995).
[Crossref]

H. S. Kim, S. H. Yun, I. K. Kwang, and B. Y. Kim, “All-fiber acousto-optic tunable notch filter with electronically controllable spectral profile,” Opt. Lett. 22, 1476–1478 (1997).
[Crossref]

H. Al-Taiy, N. Wenzel, S. Preußler, J. Klinger, and T. Schneider, “Ultra-narrow linewidth, stable and tunable laser source for optical communication systems and spectroscopy,” Opt. Lett. 39, 5826–5829 (2014).
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Photonic Sens. (1)

A. A. P. Pohl, R. A. Oliveira, R. E. da Silva, C. A. F. Marques, P. d. T. Neves, K. Cook, J. Canning, and R. N. Nogueira, “Advances and new applications using the acousto-optic effect in optical fibers,” Photonic Sens. 3, 1–25 (2013).
[Crossref]

Proc. SPIE (1)

R. Miao, W. Zhang, X. Feng, J. H. Zhao, and X. M. Liu, “All fiber tunable band-pass filter based on dual acousto-optic mode coupling,” Proc. SPIE 7134, 713434 (2008).
[Crossref]

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Figures (4)

Fig. 1
Fig. 1

The experimental configuration of the tunable fiber ring laser based on an AOTF and a TF. EDFA: erbium doped fiber amplifier. FI:fiber isolator. PC: polarization controller. AOTC: acousto-optic tunable coupler. OSA: optical spectrum analyzer. RF: radio frequency generator. SMF: single mode fiber. TF: tapered fiber.

Fig. 2
Fig. 2

(a) The wavelength tuning spectra of the output laser. (b) The tuning relationship between the output laser wavelength and the RF signal frequency with a tuning slope of −1.22 nm /kHz.

Fig. 3
Fig. 3

(a) The laser output power versus the pump current. The threshold current was 39 mA. (b) The temporal stability of the output wavelength and power. The wavelength drift was smaller than 0.1 nm and power fluctuation was smaller than 0.33 dB in one hour.

Fig. 4
Fig. 4

(a) The pulse laser spectrum. (b) The pulse train profile of the output laser. (c) The details of the laser pulses.

Equations (1)

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λ = ( n 01 co n 1 u cl ) Λ ,

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