Detailed study of four-wave mixing in Raman DFB fiber lasers

Jindan Shi; Peter Horak; Shaif-ul Alam; Morten Ibsen

doi:10.1364/OE.22.022917

Detailed study of four-wave mixing in Raman DFB fiber lasers

Jindan Shi, Peter Horak, Shaif-ul Alam, and Morten Ibsen

Optics Express
Vol. 22,
Issue 19,
pp. 22917-22924
(2014)
•https://doi.org/10.1364/OE.22.022917

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Jindan Shi, Peter Horak, Shaif-ul Alam, and Morten Ibsen, "Detailed study of four-wave mixing in Raman DFB fiber lasers," Opt. Express 22, 22917-22924 (2014)

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Related Topics
Table of Contents Category
- Lasers and Laser Optics
Optics & Photonics Topics
?

The topics in this list come from the OSA Optics and Photonics Topics applied to this article.
Previously assigned OCIS codes
- Fiber Bragg gratings (060.3735)
- Lasers, fiber (060.3510)
- Nonlinear optics, four-wave mixing (190.4380)

About this Article
History
- Original Manuscript: June 23, 2014
- Revised Manuscript: August 22, 2014
- Manuscript Accepted: August 28, 2014
- Published: September 12, 2014

Accessible

Open Access

Abstract

We both experimentally and numerically studied the ultra-compact wavelength conversion by using the four-wave mixing (FWM) process in Raman distributed-feedback (R-DFB) fiber lasers. The R-DFB fiber laser is formed in a 30 cm-long commercially available Ge/Si standard optical fiber. The internal generated R-DFB signal acts as the pump wave for the FWM process and is in the normal dispersion range of the fiber. Utilizing a tunable laser source as a probe wave, FWM frequency conversion up to ~40 THz has been demonstrated with conversion efficiency > −40 dB. The principle of such a wide bandwidth and high conversion efficiency in such a short R-DFB cavity has been theoretically analyzed. The simulation results match well with the experimental data.

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References

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Year
|
Author
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Publication

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photon. Technol. Lett. 6(8), 984–987 (1994).
[Crossref]
F. Girardin, J. Eckner, G. Guekos, R. Dall’Ara, A. Mecozzi, A. D’Ottavi, F. Martelli, S. Scotti, and P. Spano, “Low-noise and very high-efficiency four-wave mixing in 1.5-mm-long semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9(6), 746–748 (1997).
[Crossref]
H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in a long-cavity λ/4-shifted DFB laser using its lasing beam as pump beams,” IEEE J. Quantum Electron. 33(11), 2002–2010 (1997).
[Crossref]
H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “THz frequency conversion using nondegenerate four-wave mixing process in a lasing long-cavity λ/4-shifted DFB laser,” Electron. Lett. 31(24), 2108–2110 (1995).
[Crossref]
B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]
H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J.-i. Takahashi, and S.-i. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref] [PubMed]
H. Hu, C. Peucheret, M. Pu, H. Ji, M. Galili, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Wavelength conversion with large signal-idler separation using discrete four-wave mixing in a silicon nanowire,” in Proceedings of CLEO: Science and Innovations (CLEO: S and I), OSA Technical Digest (online) (Optical Society of America, 2012), CW1A.2.
[Crossref]
K. Inoue and H. Toba, “Wavelength conversion experiment using fiber four-wave mixing,” IEEE Photon. Technol. Lett. 4(1), 69–72 (1992).
[Crossref]
O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]
K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992).
[Crossref]
K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19(16), 1189–1191 (1994).
[Crossref] [PubMed]
A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30(18), 2375–2377 (2005).
[Crossref] [PubMed]
X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. Petrovich, J. Shi, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all-optical processing at telecoms wavelengths,” Opt. Fiber Technol. 16(6), 378–391 (2010).
[Crossref]
D. Méchin, R. Provo, J. D. Harvey, and C. J. McKinstrie, “180-nm wavelength conversion based on Bragg scattering in an optical fiber,” Opt. Express 14(20), 8995–8999 (2006).
[Crossref] [PubMed]
J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]
J. Shi, S. U. Alam, and M. Ibsen, “Ultra-broadband wavelength conversion based on four-wave mixing in a Raman DFB fiber laser, ” in Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper JW2A.23.
[Crossref]
J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).
J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]
M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fibre Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10(6), 842–844 (1998).
[Crossref]
G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Springer, 2000).
W. H. Loh, B. N. Samson, and J. P. de Sandro, “Intensity profile in a distributed feedback fiber laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69(25), 3773–3775 (1996).
[Crossref]
I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]
Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. 282(16), 3356–3359 (2009).
[Crossref]
Q. Zeng, “Dispersive properties in phase-shifted Bragg grating filters,” in Proceedings of Antennas and Propagation Society International Symposium (1998), Vol. 1062, pp. 1060–1063.

2013 (1)

J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]

2012 (2)

J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).

J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]

2010 (2)

X. Feng, F. Poletti, A. Camerlingo, F. Parmigiani, P. Petropoulos, P. Horak, G. M. Ponzo, M. Petrovich, J. Shi, W. H. Loh, and D. J. Richardson, “Dispersion controlled highly nonlinear fibers for all-optical processing at telecoms wavelengths,” Opt. Fiber Technol. 16(6), 378–391 (2010).
[Crossref]

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

2009 (1)

Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. 282(16), 3356–3359 (2009).
[Crossref]

2006 (1)

D. Méchin, R. Provo, J. D. Harvey, and C. J. McKinstrie, “180-nm wavelength conversion based on Bragg scattering in an optical fiber,” Opt. Express 14(20), 8995–8999 (2006).
[Crossref] [PubMed]

2005 (2)

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30(18), 2375–2377 (2005).
[Crossref] [PubMed]

H. Fukuda, K. Yamada, T. Shoji, M. Takahashi, T. Tsuchizawa, T. Watanabe, J.-i. Takahashi, and S.-i. Itabashi, “Four-wave mixing in silicon wire waveguides,” Opt. Express 13(12), 4629–4637 (2005).
[Crossref] [PubMed]

2000 (1)

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

1998 (2)

B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]

M. Ibsen, M. K. Durkin, M. J. Cole, and R. I. Laming, “Sinc-sampled fibre Bragg gratings for identical multiple wavelength operation,” IEEE Photon. Technol. Lett. 10(6), 842–844 (1998).
[Crossref]

1997 (2)

F. Girardin, J. Eckner, G. Guekos, R. Dall’Ara, A. Mecozzi, A. D’Ottavi, F. Martelli, S. Scotti, and P. Spano, “Low-noise and very high-efficiency four-wave mixing in 1.5-mm-long semiconductor optical amplifiers,” IEEE Photon. Technol. Lett. 9(6), 746–748 (1997).
[Crossref]

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “Nondegenerate four-wave mixing in a long-cavity λ/4-shifted DFB laser using its lasing beam as pump beams,” IEEE J. Quantum Electron. 33(11), 2002–2010 (1997).
[Crossref]

1996 (1)

W. H. Loh, B. N. Samson, and J. P. de Sandro, “Intensity profile in a distributed feedback fiber laser characterized by a green fluorescence scanning technique,” Appl. Phys. Lett. 69(25), 3773–3775 (1996).
[Crossref]

1995 (1)

H. Kuwatsuka, H. Shoji, M. Matsuda, and H. Ishikawa, “THz frequency conversion using nondegenerate four-wave mixing process in a lasing long-cavity λ/4-shifted DFB laser,” Electron. Lett. 31(24), 2108–2110 (1995).
[Crossref]

1994 (2)

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photon. Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19(16), 1189–1191 (1994).
[Crossref] [PubMed]

1992 (2)

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992).
[Crossref]

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber four-wave mixing,” IEEE Photon. Technol. Lett. 4(1), 69–72 (1992).
[Crossref]

Alam, S. U.

J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]

J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]

Alam, S.-U.

J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).

Arai, S.-I.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Aso, O.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Broderick, N. G. R.

Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. 282(16), 3356–3359 (2009).
[Crossref]

Camerlingo, A.

Cole, M. J.

D’Ottavi, A.

Dall’Ara, R.

de Sandro, J. P.

De Sterke, C. M.

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

Demokan, M. S.

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30(18), 2375–2377 (2005).
[Crossref] [PubMed]

Durkin, M. K.

Eckner, J.

Eggleton, B. J.

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

Feng, X.

Fukuda, H.

Girardin, F.

Guekos, G.

Harvey, J. D.

Horak, P.

Hu, Y.

Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. 282(16), 3356–3359 (2009).
[Crossref]

Ibsen, M.

J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]

J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).

J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]

Inoue, K.

K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19(16), 1189–1191 (1994).
[Crossref] [PubMed]

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber four-wave mixing,” IEEE Photon. Technol. Lett. 4(1), 69–72 (1992).
[Crossref]

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992).
[Crossref]

Ishikawa, H.

B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]

Itabashi, S.-i.

Kabakova, I. V.

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

Kuwatsuka, H.

B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]

Laming, R. I.

Little, B. E.

B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]

Loh, W. H.

Martelli, F.

Matsuda, M.

McKinstrie, C. J.

Méchin, D.

Mecozzi, A.

Miller, B. I.

Namiki, S.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Newkirk, M. A.

Park, N.

Parmigiani, F.

Petropoulos, P.

Petrovich, M.

Poletti, F.

Ponzo, G. M.

Provo, R.

Richardson, D. J.

Samson, B. N.

Scotti, S.

Shi, J.

J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]

J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]

J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).

Shoji, H.

Shoji, T.

Spano, P.

Suzuki, Y.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Tadakuma, M.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Takahashi, J.-i.

Takahashi, M.

Toba, H.

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber four-wave mixing,” IEEE Photon. Technol. Lett. 4(1), 69–72 (1992).
[Crossref]

Tsuchizawa, T.

Vahala, K. J.

Walsh, T.

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

Watanabe, T.

Yagi, T.

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

Yamada, K.

Zhang, A.

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30(18), 2375–2377 (2005).
[Crossref] [PubMed]

Zhou, J.

Appl. Phys. Lett. (1)

Electron. Lett. (2)

O. Aso, S.-I. Arai, T. Yagi, M. Tadakuma, Y. Suzuki, and S. Namiki, “Broadband four-wave mixing generation in short optical fibres,” Electron. Lett. 36(8), 709–711 (2000).
[Crossref]

IEEE J. Quantum Electron. (1)

IEEE Photon. Technol. Lett. (5)

K. Inoue and H. Toba, “Wavelength conversion experiment using fiber four-wave mixing,” IEEE Photon. Technol. Lett. 4(1), 69–72 (1992).
[Crossref]

B. E. Little, H. Kuwatsuka, and H. Ishikawa, “Nondegenerate four-wave mixing efficiencies in DFB laser wavelength converters,” IEEE Photon. Technol. Lett. 10(4), 519–521 (1998).
[Crossref]

J. Lightwave Technol. (1)

K. Inoue, “Four-wave mixing in an optical fiber in the zero-dispersion wavelength region,” J. Lightwave Technol. 10(11), 1553–1561 (1992).
[Crossref]

J. Opt. Soc. Am. B (1)

I. V. Kabakova, T. Walsh, C. M. De Sterke, and B. J. Eggleton, “Performance of field-enhanced optical switching in fiber Bragg gratings,” J. Opt. Soc. Am. B 27(7), 1343–1351 (2010).
[Crossref]

Opt. Commun. (1)

Y. Hu and N. G. R. Broderick, “Improved design of a DFB Raman fibre laser,” Opt. Commun. 282(16), 3356–3359 (2009).
[Crossref]

Opt. Express (3)

J. Shi, S. U. Alam, and M. Ibsen, “Highly efficient Raman distributed feedback fibre lasers,” Opt. Express 20(5), 5082–5091 (2012).
[Crossref] [PubMed]

Opt. Fiber Technol. (1)

Opt. Lett. (4)

J. Shi, S.-U. Alam, and M. Ibsen, “Sub-watt threshold, kilohertz-linewidth Raman distributed-feedback fiber laser,” Opt. Lett. 37(9), 1544–1546 (2012).

J. Shi, S. U. Alam, and M. Ibsen, “Ultrawide-range four-wave mixing in Raman distributed-feedback fiber lasers,” Opt. Lett. 38(6), 944–946 (2013).
[Crossref] [PubMed]

K. Inoue, “Arrangement of fiber pieces for a wide wavelength conversion range by fiber four-wave mixing,” Opt. Lett. 19(16), 1189–1191 (1994).
[Crossref] [PubMed]

A. Zhang and M. S. Demokan, “Broadband wavelength converter based on four-wave mixing in a highly nonlinear photonic crystal fiber,” Opt. Lett. 30(18), 2375–2377 (2005).
[Crossref] [PubMed]

Other (4)

J. Shi, S. U. Alam, and M. Ibsen, “Ultra-broadband wavelength conversion based on four-wave mixing in a Raman DFB fiber laser, ” in Proceedings of Optical Fiber Communication Conference/National Fiber Optic Engineers Conference 2013, OSA Technical Digest (online) (Optical Society of America, 2013), paper JW2A.23.
[Crossref]

H. Hu, C. Peucheret, M. Pu, H. Ji, M. Galili, K. Yvind, J. M. Hvam, P. Jeppesen, and L. K. Oxenløwe, “Wavelength conversion with large signal-idler separation using discrete four-wave mixing in a silicon nanowire,” in Proceedings of CLEO: Science and Innovations (CLEO: S and I), OSA Technical Digest (online) (Optical Society of America, 2012), CW1A.2.
[Crossref]

G. Agrawal, Nonlinear Fiber Optics, 3rd ed. (Springer, 2000).

Q. Zeng, “Dispersive properties in phase-shifted Bragg grating filters,” in Proceedings of Antennas and Propagation Society International Symposium (1998), Vol. 1062, pp. 1060–1063.

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Fig. 1 Schematic diagram of experimental setup for FWM generation in a R-DFB fiber laser. ISO: isolator; PC: polarization controller; WDM: wavelength division multiplexer; TLS: tunable laser source; YDFA: Yb-doped fiber amplifier; OSA: optical spectrum analyzer.

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Fig. 2 (a) FWM output spectra with a resolution of 1 nm and (b) normalized overlapping spectra of the probe wave #2 and corresponding conjugate wave #2* with a resolution of 0.01 nm.

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Fig. 3 (a) FWM conversion efficiency of the R-DFB fiber laser with respect to the frequency detuning. The vertical lines indicate the probe waves of #i (i = 0,1,2,3,4,5). (b) FWM conversion efficiency against incident probe power for probe waves of #1, #2, #3, #4, and #5, respectively.

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Fig. 4 Schematic diagram of theoretical model setup for FWM in R-DFB fiber laser.

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Fig. 5 (a) Calculated FWM conversion efficiency in the 30 cm long R-DFB fiber laser and a similar length of PS980 fiber, respectively; (b) Calculated dispersion profile of the PS980 fiber (inset shows the calculated dispersion of the R-DFB grating).

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Fig. 6 (a) Comparison of the experimental and calculated FWM conversion efficiency against frequency detuning; (b) Calculated FWM conversion efficiency against probe power from several mW to 5 W.

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Fig. 7 Calculated FWM conversion efficiency against (a) coupling coefficient of the DFB grating and (b) length of the DFB grating.

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Tables (1)

Table 1 Main parameters applied for FWM simulation in the R-DFB fiber laser

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Equations (6)

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A_{1 f} (z) = {\begin{matrix} A_{1 f} (z = L) \cdot \sin h (κ z) z < L / 2 \\ A_{1 f} (z = L) \cdot \cos h [κ (L - z)] z > L / 2 \\ A_{1 f} (z = L) \cdot [\sin h (κ L / 2) + \cos h (κ L / 2)] / 2 z = L / 2 \end{matrix}

A_{1 b} (z) = {\begin{matrix} A_{1 b} (z = 0) \cdot \cos h (κ z) z < L / 2 \\ A_{1 b} (z = 0) \cdot \sin h [κ (L - z)] z > L / 2 \\ A_{1 b} (z = 0) \cdot [\sin h (κ L / 2) + \cos h (κ L / 2)] / 2 z = L / 2 \end{matrix}

d A_{3} / d z = i γ_{3} [({| A_{3} |}^{2} + 2 {| A_{1 f} |}^{2} + 2 {| A_{1 b} |}^{2} + 2 {| A_{4} |}^{2}) \cdot A_{3} + A_{1 f}^{2} A_{4}^{*} e^{- i (δ k) z}] - α_{3} A_{3} / 2

d A_{4} / d z = i γ_{4} [({| A_{4} |}^{2} + 2 {| A_{1 f} |}^{2} + 2 {| A_{1 b} |}^{2} + 2 {| A_{3} |}^{2}) \cdot A_{4} + A_{1 f}^{2} A_{3}^{*} e^{- i (δ k) z}] - α_{4} A_{4} / 2

\begin{array}{l} A_{1 f} (z = L) = A_{1 b} (z = 0) = \sqrt{P_{1 f} (z = L) / A_{e f f}} \\ A_{3} (z = 0) = \sqrt{P_{3} (z = 0) / A_{e f f}} \\ A_{4} (z = 0) = 0 \end{array}

η = P_{4} (z = L) / P_{3} (z = 0)

Parameter	$P_{1 f} (z = L)$ (mW)	$P_{3} (z = 0)$ (mW)	$κ$ (m⁻¹)	$A_{e f f}$ (μm²)	$n_{2}$ (m²/W)	L (cm)	$α$ (dB/km)
Value	60	50	37	35	3.2x10⁻²⁰	30	20