Abstract

An alternative of the long-period fiber grating (LPFG) fabrication method has been developed in this work by use of defocused CO2 laser pulse scanning, which is achieved by moving the laser beam focus plane slightly away from the fiber cladding surface. By increasing the distance shift from the cladding surface, the area with refractive index change also increases on the side with laser irradiation, which leads to an apparent mode field profile distortion at the resonant wavelength of the LPFG. Such a distortion in the mode field profile significantly increases the polarization-dependent loss of the LPFG. Moreover, for the cascaded LPFGs fabricated by use of this technique, the maximum polarization-dependent loss obtained can be largely increased from 7to17.8dB, with a maximum dip in the wavelength change of 0.45nm.

© 2009 Optical Society of America

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    [CrossRef]
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    [CrossRef]
  4. Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
    [CrossRef]
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    [CrossRef]
  6. A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]

2008

H. F. Xuan, W. Jin, J. Ju, Y. P. Wang, M. Zhang, Y. B. Liao, and M. H. Chen, “Hollow-core photonic bandgap fiber polarizer,” Opt. Lett. 33, 845-847 (2008).
[CrossRef] [PubMed]

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

2007

R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. 275, 90-93 (2007).
[CrossRef]

M. Yan, S. Y. Luo, L. Zhan, Z. M. Zhang, and Yuxing Xia, “Triple-wavelength switchable Erbium-doped fiber laser with cascaded asymmetric exposure long-period fiber gratings,” Opt. Express 15, 3685-3691 (2007).
[CrossRef] [PubMed]

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Y. P. Wang, L. M. Xiao, D. N. Wang, and W. Jin, “In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber,” Opt. Lett. 32, 1035-1037 (2007).
[CrossRef] [PubMed]

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “A highly sensitive fiber-optic refractive index sensor based on an edge-written long-period fiber grating,” IEEE Photon. Technol. Lett. 19, 1946-1948 (2007).
[CrossRef]

2006

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

2003

2002

2001

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

1998

D. D. Davis, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416-1417 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

1997

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Ahn, T.-J.

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

Bachim, B. L.

B. L. Bachim and T. K. Gaylord, “Polarization-dependent loss and birefringence in long-period fiber gratings,” Appl. Opt. 42, 6818-6823 (2003).
[CrossRef]

Bayon, J. F.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Bennion, I.

Chen, M. H.

Cheong, J.

Chung, Y.

Davis, D. D.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416-1417 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Douay, M.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Duhem, O.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Gaylord, T. K.

B. L. Bachim and T. K. Gaylord, “Polarization-dependent loss and birefringence in long-period fiber gratings,” Appl. Opt. 42, 6818-6823 (2003).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416-1417 (1998).
[CrossRef]

Glytsis, E. N.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416-1417 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Han, W.-T.

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

Henninot, J. F.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Hirose, T.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Ho, H. L.

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

Ikushima, A. J.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Jin, W.

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

H. F. Xuan, W. Jin, J. Ju, Y. P. Wang, M. Zhang, Y. B. Liao, and M. H. Chen, “Hollow-core photonic bandgap fiber polarizer,” Opt. Lett. 33, 845-847 (2008).
[CrossRef] [PubMed]

Y. P. Wang, L. M. Xiao, D. N. Wang, and W. Jin, “In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber,” Opt. Lett. 32, 1035-1037 (2007).
[CrossRef] [PubMed]

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Ju, J.

H. F. Xuan, W. Jin, J. Ju, Y. P. Wang, M. Zhang, Y. B. Liao, and M. H. Chen, “Hollow-core photonic bandgap fiber polarizer,” Opt. Lett. 33, 845-847 (2008).
[CrossRef] [PubMed]

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

Kim, B. H.

Kim, B.-H.

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

Kim, D. Y.

Kojima, S.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Kosinski, S. G.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Kurkov, A. S.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Lee, B.

Y. W. Lee and B. Lee, “Wavelength-switchable erbium-doped fiber ring laser using spectral polarization-dependent loss element,” IEEE Photon. Technol. Lett. 15, 795-797 (2003).
[CrossRef]

B. Lee, J. Cheong, and U. Paek, “Spectral polarization-dependent loss of cascaded long-period fiber gratings,” Opt. Lett. 27, 1096-1098 (2002).
[CrossRef]

Lee, B. H.

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

Lee, Y. W.

Y. W. Lee and B. Lee, “Wavelength-switchable erbium-doped fiber ring laser using spectral polarization-dependent loss element,” IEEE Photon. Technol. Lett. 15, 795-797 (2003).
[CrossRef]

Leleu, B.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Liao, Y. B.

Luo, S. Y.

Mettler, S. C.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, and S. C. Mettler, “CO2 laser-induced long-period fiber gratings: spectral characteristics, cladding modes and polarization independence,” Electron. Lett. 34, 1416-1417 (1998).
[CrossRef]

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Oh, S. T.

Ohsono, K.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Paek, U.

Paek, U. C.

B. H. Kim, Y. Park, T.-J. Ahn, D. Y. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Residual stress relaxation in the core of optical fiber by CO2 laser irradiation,” Opt. Lett. 26, 1657-1659 (2001).
[CrossRef]

T.-J. Ahn, B.-H. Kim, B. H. Lee, Y. Chung, U. C. Paek, and W.-T. Han, “Torsion sensing characteristics of optical fiber with a long-period grating pair,” Proc. SPIE 4579, 154-161 (2001).
[CrossRef]

Park, Y.

Peng, G. D.

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Ran, Z. L.

Rao, Y. J.

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “A highly sensitive fiber-optic refractive index sensor based on an edge-written long-period fiber grating,” IEEE Photon. Technol. Lett. 19, 1946-1948 (2007).
[CrossRef]

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Rivoallan, L.

A. S. Kurkov, M. Douay, O. Duhem, B. Leleu, J. F. Henninot, J. F. Bayon, and L. Rivoallan, “Long-period fiber grating as a wavelength selective polarization element,” Electron. Lett. 33, 616-617 (1997).
[CrossRef]

Ryu, H. S.

Saito, K.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Sato, S.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Shu, X. W.

Slavik, R.

R. Slavik, “Coupling to circularly asymmetric modes via long-period gratings made in a standard straight fiber,” Opt. Commun. 275, 90-93 (2007).
[CrossRef]

Song, Y.

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “A highly sensitive fiber-optic refractive index sensor based on an edge-written long-period fiber grating,” IEEE Photon. Technol. Lett. 19, 1946-1948 (2007).
[CrossRef]

Takada, K.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Vengsarkar, A. M.

D. D. Davis, T. K. Gaylord, E. N. Glytsis, S. G. Kosinski, S. C. Mettler, and A. M. Vengsarkar, “Long-period fiber-grating fabrication with focused CO2 laser pulses,” Electron. Lett. 34, 302-303 (1998).
[CrossRef]

Wang, D. N.

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

Y. P. Wang, L. M. Xiao, D. N. Wang, and W. Jin, “In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber,” Opt. Lett. 32, 1035-1037 (2007).
[CrossRef] [PubMed]

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Wang, J. L.

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “A highly sensitive fiber-optic refractive index sensor based on an edge-written long-period fiber grating,” IEEE Photon. Technol. Lett. 19, 1946-1948 (2007).
[CrossRef]

Wang, Y. P.

Y. P. Wang, D. N. Wang, W. Jin, H. L. Ho, and J. Ju, “Mode field profile and polarization dependence of long-period fiber gratings written by CO2 laser,” Opt. Commun. 281, 2522-2525 (2008).
[CrossRef]

H. F. Xuan, W. Jin, J. Ju, Y. P. Wang, M. Zhang, Y. B. Liao, and M. H. Chen, “Hollow-core photonic bandgap fiber polarizer,” Opt. Lett. 33, 845-847 (2008).
[CrossRef] [PubMed]

Y. P. Wang, L. M. Xiao, D. N. Wang, and W. Jin, “In-fiber polarizer based on a long-period fiber grating written on photonic crystal fiber,” Opt. Lett. 32, 1035-1037 (2007).
[CrossRef] [PubMed]

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Xia, Yuxing

Xiao, L. M.

Xuan, H. F.

Yan, M.

Yao, B.

T. Hirose, K. Saito, S. Kojima, B. Yao, K. Ohsono, S. Sato, K. Takada, and A. J. Ikushima, “Fabrication of long-period fiber grating by CO2 laser-annealing in fiber-drawing process,” Electron. Lett. 43, 443-445 (2007).
[CrossRef]

Zhan, L.

Zhang, L.

Zhang, M.

Zhang, Z. M.

Zhu, T.

T. Zhu, Y. J. Rao, J. L. Wang, and Y. Song, “A highly sensitive fiber-optic refractive index sensor based on an edge-written long-period fiber grating,” IEEE Photon. Technol. Lett. 19, 1946-1948 (2007).
[CrossRef]

Y. J. Rao, Y. P. Wang, Z. L. Ran, and T. Zhu, “Novel fiber-optic sensors based on long-period fiber gratings written by high-frequency CO2 laser pulses,” J. Lightwave Technol. 21, 1320-1327 (2003).
[CrossRef]

Appl. Opt.

B. L. Bachim and T. K. Gaylord, “Polarization-dependent loss and birefringence in long-period fiber gratings,” Appl. Opt. 42, 6818-6823 (2003).
[CrossRef]

Appl. Phys. Lett.

Y. P. Wang, D. N. Wang, W. Jin, Y. J. Rao, and G. D. Peng, “Asymmetric long-period fiber gratings fabricated by use of CO2 laser to carve periodic grooves on the optical fiber,” Appl. Phys. Lett. 89, 151105-151108 (2006).
[CrossRef]

Electron. Lett.

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Figures (6)

Fig. 1
Fig. 1

Fabrication of LPFG with defocused high-frequency C O 2 laser.

Fig. 2
Fig. 2

CCD figures of the cladding surface for LPFGs made by different defocused lengths (a) 0 mm , (b) 1 mm , (c) 2 mm .

Fig. 3
Fig. 3

PDL test of LPFGs with defocused lengths (a) 0 mm , (b) 1 mm , (c) 2 mm .

Fig. 4
Fig. 4

Mode distortion of excited cladding mode of LPFGs with defocused lengths (a) 0 mm , (b) 1 mm , (c) 2 mm .

Fig. 5
Fig. 5

PDL test of CLPFGs with different defocused lengths (a) 0 mm and (b) 2 mm , and the polarization-induced minimum and maximum transmitted power of CLPFGs with different defocused lengths (c) 0 mm and (d) 2 mm .

Fig. 6
Fig. 6

Simulated LP 16 mode profile with (a) none, (b) linear, (c) quadratic, and (d) exponential side cladding refractive-index change.

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