Abstract

An approach to reconstruct a quasi-phase-matching grating by using a discrete layer-peeling algorithm is presented. Experimentally measured output spectra of Šolc-type filters, based on uniform and chirped QPM structures, are used in the discrete layer-peeling algorithm. The reconstructed QPM structures are in agreement with the exact structures used in the experiment and the method is verified to be accurate and efficient in quality inspection on quasi-phase-matching grating.

© 2012 OSA

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
    [CrossRef]
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    [CrossRef]
  28. G. Lenz, B. J. Eggleton, and C. R. Giles, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
    [CrossRef]
  29. L. Wang and T. Erdogan, “Layer peeling algorithm for reconstruction of long-period fibre gratings,” Electron. Lett. 37, 154–156 (2001).
    [CrossRef]
  30. T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
    [CrossRef]
  31. R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted co-directional mode couplers,” J. Opt. Soc. Am. A 17, 1573–1582 (2000).
    [CrossRef]
  32. O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
    [CrossRef]

2012 (1)

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

2011 (1)

2009 (2)

2008 (6)

2007 (2)

2006 (2)

2005 (1)

2004 (3)

2003 (3)

J. K. Brenne and J. Skaar, “Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms,” J. Lightwave. Technol. 21, 254–263 (2003).
[CrossRef]

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Šolc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[CrossRef] [PubMed]

2002 (3)

2001 (2)

J. Shaar, L. G. Wang, and T. Erdogan, “On the synthesis of fiber bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

L. Wang and T. Erdogan, “Layer peeling algorithm for reconstruction of long-period fibre gratings,” Electron. Lett. 37, 154–156 (2001).
[CrossRef]

2000 (2)

R. Feced and M. N. Zervas, “Efficient inverse scattering algorithm for the design of grating-assisted co-directional mode couplers,” J. Opt. Soc. Am. A 17, 1573–1582 (2000).
[CrossRef]

Y. Q. Lu and Z. L. Wan, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

1998 (1)

G. Lenz, B. J. Eggleton, and C. R. Giles, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

1997 (2)

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

1994 (1)

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the Phase-Matching Bandwidth in Quasi-Phase-Matched Second-Harmoic Generation,” IEEE J. Quantum Electron. 30, 1596–1604 (1994).
[CrossRef]

Afeyan, B.

Arie, A.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Ashihara, S.

X. Zeng, S. Ashihara, Z. Wang, T. Wang, Y. Chen, and M. Cha, “Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure, ” Opt. Express 17, 16877–16884 (2009).
[CrossRef] [PubMed]

X. Zeng, S. Ashihara, X. Chen, T. Shimura, and K. Kuroda, “Two-color pulse compression in aperiodically poled lithium niobate,” Opt. Commun. 281, 4499–4503 (2008).
[CrossRef]

Asobe, M.

Bae, J.

Beckwitt, K.

Brenne, J. K.

J. K. Brenne and J. Skaar, “Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms,” J. Lightwave. Technol. 21, 254–263 (2003).
[CrossRef]

Cha, M.

Chang, C. L.

Chang, J. Y.

Charbonneau-Lefort, M.

Chen, X.

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

X. Zeng, S. Ashihara, X. Chen, T. Shimura, and K. Kuroda, “Two-color pulse compression in aperiodically poled lithium niobate,” Opt. Commun. 281, 4499–4503 (2008).
[CrossRef]

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Šolc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[CrossRef] [PubMed]

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

Chen, Y.

X. Zeng, S. Ashihara, Z. Wang, T. Wang, Y. Chen, and M. Cha, “Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure, ” Opt. Express 17, 16877–16884 (2009).
[CrossRef] [PubMed]

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Šolc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[CrossRef] [PubMed]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Šolc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[CrossRef] [PubMed]

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

Chen, Y. H.

Cheng, X. P.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Choi, Y.

Chou, M. H.

Chun, J.

Dong, B. Z.

Eggleton, B. J.

G. Lenz, B. J. Eggleton, and C. R. Giles, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Erdogan, T.

L. Wang and T. Erdogan, “Layer peeling algorithm for reconstruction of long-period fibre gratings,” Electron. Lett. 37, 154–156 (2001).
[CrossRef]

J. Shaar, L. G. Wang, and T. Erdogan, “On the synthesis of fiber bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

T. Erdogan, “Fiber grating spectra,” J. Lightwave Technol. 15, 1277–1294 (1997).
[CrossRef]

Fan, F. C.

Feced, R.

Fejer, M. M.

Galun, E.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Gayer, O.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Giles, C. R.

G. Lenz, B. J. Eggleton, and C. R. Giles, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Gu, B. Y.

Gu, X.

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

Horowitz, M.

Huang, C. Y.

Huang, J.

Huang, Y. C.

Hum, D. S.

Ilday, F. Ö.

Imeshev, G.

Jung, C.

Kato, M.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the Phase-Matching Bandwidth in Quasi-Phase-Matched Second-Harmoic Generation,” IEEE J. Quantum Electron. 30, 1596–1604 (1994).
[CrossRef]

Kee, C. S.

Ko, D. K.

Kumagai, T.

Kuroda, K.

X. Zeng, S. Ashihara, X. Chen, T. Shimura, and K. Kuroda, “Two-color pulse compression in aperiodically poled lithium niobate,” Opt. Commun. 281, 4499–4503 (2008).
[CrossRef]

Langrock, C.

Lee, J.

Lee, Y. L.

Lee, Y. W.

Lenz, G.

G. Lenz, B. J. Eggleton, and C. R. Giles, “Dispersive properties of optical filters for WDM systems,” IEEE J. Quantum Electron. 34, 1390–1402 (1998).
[CrossRef]

Levy, E. C.

Li, H.

Li, S. Y.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Lin, C. H.

Lin, S. W.

Lu, Y. Q.

Y. Q. Lu and Z. L. Wan, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Magari, K.

Miao, H.

Ming, N. B.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

Mizuuchi, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the Phase-Matching Bandwidth in Quasi-Phase-Matched Second-Harmoic Generation,” IEEE J. Quantum Electron. 30, 1596–1604 (1994).
[CrossRef]

Ng, J. H.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Ngo, N. Q.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Nishida, Y.

Noh, Y. C.

Ogusu, K.

Pang, F.

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

Roussev, R. V.

Sacks, Z.

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Sato, H.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the Phase-Matching Bandwidth in Quasi-Phase-Matched Second-Harmoic Generation,” IEEE J. Quantum Electron. 30, 1596–1604 (1994).
[CrossRef]

Schober, A. M.

Shaar, J.

J. Shaar, L. G. Wang, and T. Erdogan, “On the synthesis of fiber bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Shi, J.

Shimura, T.

X. Zeng, S. Ashihara, X. Chen, T. Shimura, and K. Kuroda, “Two-color pulse compression in aperiodically poled lithium niobate,” Opt. Commun. 281, 4499–4503 (2008).
[CrossRef]

Shin, W.

Shum, P.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Skaar, J.

J. K. Brenne and J. Skaar, “Design of grating-assisted codirectional couplers with discrete inverse-scattering algorithms,” J. Lightwave. Technol. 21, 254–263 (2003).
[CrossRef]

Suzuki, H.

Tadanaga, O.

Umeki, T.

Wan, Z. L.

Y. Q. Lu and Z. L. Wan, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Wang, L.

L. Wang and T. Erdogan, “Layer peeling algorithm for reconstruction of long-period fibre gratings,” Electron. Lett. 37, 154–156 (2001).
[CrossRef]

Wang, L. G.

J. Shaar, L. G. Wang, and T. Erdogan, “On the synthesis of fiber bragg gratings by layer peeling,” IEEE J. Quantum Electron. 37, 165–173 (2001).
[CrossRef]

Wang, T.

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

X. Zeng, S. Ashihara, Z. Wang, T. Wang, Y. Chen, and M. Cha, “Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure, ” Opt. Express 17, 16877–16884 (2009).
[CrossRef] [PubMed]

Wang, Z.

Weiner, A. M.

Wise, F. W.

Wu, F.

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

Xia, Y.

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

X. Chen, J. Shi, Y. Chen, Y. Zhu, Y. Xia, and Y. Chen, “Electro-optic Šolc-type wavelength filter in periodically poled lithium niobate,” Opt. Lett. 28, 2115–2117 (2003).
[CrossRef] [PubMed]

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

Xie, X. P.

Yamamoto, K.

K. Mizuuchi, K. Yamamoto, M. Kato, and H. Sato, “Broadening of the Phase-Matching Bandwidth in Quasi-Phase-Matched Second-Harmoic Generation,” IEEE J. Quantum Electron. 30, 1596–1604 (1994).
[CrossRef]

Yanagawa, T.

Yang, S.

Yu, N. E.

Zeng, X.

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

X. Zeng, S. Ashihara, Z. Wang, T. Wang, Y. Chen, and M. Cha, “Excitation of two-colored temporal solitons in a segmented quasi-phase-matching structure, ” Opt. Express 17, 16877–16884 (2009).
[CrossRef] [PubMed]

X. Zeng, S. Ashihara, X. Chen, T. Shimura, and K. Kuroda, “Two-color pulse compression in aperiodically poled lithium niobate,” Opt. Commun. 281, 4499–4503 (2008).
[CrossRef]

X. Gu, X. Chen, Y. Chen, X. Zeng, Y. Xia, and Y. Chen, “Narrowband multiple wavelengths filter in aperiodic optical superlattice,” Opt. Commun. 237, 53–58 (2004).
[CrossRef]

X. Zeng, X. Chen, F. Wu, Y. Chen, Y. Xia, and Y. Chen, “Second-harmonic generation with broadened flattop bandwidth in aperiodic domain-inverted gratings,” Opt. Commun. 204, 407–411 (2002).
[CrossRef]

Zervas, M. N.

Zhang, J.

J. Zhang, P. Shum, S. Y. Li, N. Q. Ngo, X. P. Cheng, and J. H. Ng, “Design and fabrication of flat-band long-period grating,” IEEE Photon. Technol. Lett. 15, 1558–1560 (2003).
[CrossRef]

Zhang, Q.

Q. Zhang, X. Zeng, F. Pang, X. Chen, and T. Wang, “Tunable polarization-independent Šolc-type wavelength filter based on periodically poled lithium niobate,” Opt. Laser Technol. 44, 1992–1994 (2012).
[CrossRef]

Zhu, S. N.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

Zhu, Y.

Zhu, Y. Y.

S. N. Zhu, Y. Y. Zhu, and N. B. Ming, “Quasi-phase-matched third-harmonic generation in a quasi-periodic optical superlattice,” Science 278, 843–846 (1997).
[CrossRef]

Appl. Phys. B (1)

O. Gayer, Z. Sacks, E. Galun, and A. Arie, “Temperature and wavelength dependent refractive index equations for MgO-doped congruent and stoichiometric LiNbO3,” Appl. Phys. B 91, 343–348 (2008).
[CrossRef]

Appl. Phys. Lett. (1)

Y. Q. Lu and Z. L. Wan, “Electro-optic effect of periodically poled optical superlattice LiNbO3 and its applications,” Appl. Phys. Lett. 77, 3719–3721 (2000).
[CrossRef]

Electron. Lett. (1)

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Figures (5)

Fig. 1
Fig. 1

The discretized coupling model of ordinary and extraordinary waves based on QPM structure.

Fig. 2
Fig. 2

(a) Experimental setup of tunable Šolc filter based on QPM structure; (b) the output spectrum of C+L broadband ASE source.

Fig. 3
Fig. 3

(a) Normalized transmission spectrum at 35.5°C based on uniform QPM grating; (b) comparison between the reconstructed and the nominal uniform QPM gratings.

Fig. 4
Fig. 4

Normalized transmission spectra (a) linearly chirped grating at 55°C; (b) quadratically chirped grating at 60°C.

Fig. 5
Fig. 5

Comparison between the reconstructed and nominal linearly and quadratically chirped QPM gratings.

Equations (8)

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d A o ( z , Δ β ) d z = i κ ( z ) A e exp ( i Δ β z )
d A e ( z , Δ β ) d z = i κ * ( z ) A o exp ( i Δ β z )
[ A o , j + 1 ( Δ β ) A e , j + 1 ( Δ β ) ] = G Δ G ρ [ A o , j ( Δ β ) A e , j ( Δ β ) ]
κ ( z j ) = 1 Δ z ρ j * | ρ j | arctan ( | ρ j | )
A o ( e ) , j ( Δ β ) = τ = 0 N a o ( e ) , j ( τ ) exp ( i 2 Δ β Δ z τ )
a o ( e ) , j ( τ ) = [ a o ( e ) , j ( 0 ) a o ( e ) , j ( 1 ) a o ( e ) , j ( N ) ]
ρ N = a e , N ( 0 ) a o , N ( 0 )
d ϕ ( z j ) d z = 2 π z j Λ j 2 d Λ j d z

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