Abstract

High order resonances between fundamental core mode and cladding LP01 supermodes are demonstrated in long period fiber gratings (LPFGs) inscribed in all-solid photonic bandgap fibers for the first time to our knowledge. The resonance wavelengths of the LPFGs calculated by way of photonic bandgap theory agree with the experimental results. The temperature responses of these resonance peaks have been theoretically and experimentally investigated. In addition, the mechanism of LPFG formation has been researched deeply through coupled-mode theory (CMT) and the cutback experiments.

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  1. X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
    [CrossRef]
  2. T. Zhu, Y. J. Rao, and J. L. Wang, “Characteristics of novel ultra-long-period fiber gratings fabricated by high-frequency CO2 laser pulses,” Opt. Commun. 277(1), 84–88 (2007).
    [CrossRef]
  3. T. B. Iredale, P. Steinvurzel, and B. J. Eggleton, “Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre,” Electron. Lett. 42(13), 739–740 (2006).
    [CrossRef]
  4. D. I. Yeom, P. Steinvurzel, B. J. Eggleton, S. D. Lim, and B. Y. Kim, “Tunable acoustic gratings in solid-core photonic bandgap fiber,” Opt. Express 15(6), 3513–3518 (2007).
    [CrossRef] [PubMed]
  5. Q. Shi and B. T. Kuhlmey, “Optimization of photonic bandgap fiber long period grating refractive-index sensors,” Opt. Commun. 282(24), 4723–4728 (2009).
    [CrossRef]
  6. L. Jin, Z. Wang, Y. G. Liu, G. Y. Kai, and X. Y. Dong, “Ultraviolet-inscribed long period gratings in all-solid photonic bandgap fibers,” Opt. Express 16(25), 21119–21131 (2008).
    [CrossRef] [PubMed]
  7. D. Noordegraaf, L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, “Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers,” Opt. Express 15(13), 7901–7912 (2007).
    [CrossRef] [PubMed]
  8. L. Wei, J. Weirich, T. T. Alkeskjold, and A. Bjarklev, “On-chip tunable long-period grating devices based on liquid crystal photonic bandgap fibers,” Opt. Lett. 34(24), 3818–3820 (2009).
    [CrossRef] [PubMed]
  9. P. Steinvurzel, E. D. Moore, E. C. Mägi, and B. J. Eggleton, “Tuning properties of long period gratings in photonic bandgap fibers,” Opt. Lett. 31(14), 2103–2105 (2006).
    [CrossRef] [PubMed]
  10. P. Steinvurzel, E. D. Moore, E. C. Mägi, B. T. Kuhlmey, and B. J. Eggleton, “Long period grating resonances in photonic bandgap fiber,” Opt. Express 14(7), 3007–3014 (2006).
    [CrossRef] [PubMed]
  11. M. W. Yang, D. N. Wang, Y. Wang, and C. R. Liao, “Long period fiber grating formed by periodically structured microholes in all-solid photonic bandgap fiber,” Opt. Express 18(3), 2183–2189 (2010).
    [CrossRef] [PubMed]
  12. C. R. Liao, Y. Wang, D. N. Wang, and L. Jin, “Femtosecond Laser Inscribed Long-Period Gratings in All-Solid Photonic Bandgap Fibers,” IEEE Photon. Technol. Lett. 22(6), 425–427 (2010).
    [CrossRef]
  13. Y. P. Wang, W. Jin, J. Ju, H. F. Xuan, H. L. Ho, L. M. Xiao, and D. N. Wang, “Long period gratings in air-core photonic bandgap fibers,” Opt. Express 16(4), 2784–2790 (2008).
    [CrossRef] [PubMed]
  14. L. Jin, Z. Wang, Q. Fang, Y. Liu, B. Liu, G. Y. Kai, and X. Y. Dong, “Spectral characteristics and bend response of Bragg gratings inscribed in all-solid bandgap fibers,” Opt. Express 15(23), 15555–15565 (2007).
    [CrossRef] [PubMed]
  15. B. T. Kuhlmey, F. Luan, L. B. Fu, D. I. Yeom, B. J. Eggleton, A. M. Wang, and J. C. Knight, “Experimental reconstruction of bands in solid core photonic bandgap fibres using acoustic gratings,” Opt. Express 16(18), 13845–13856 (2008).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
  17. S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
    [CrossRef] [PubMed]
  18. V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
    [CrossRef]
  19. X. W. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002).
    [CrossRef]
  20. 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 CO(2) laser irradiation,” Opt. Lett. 26(21), 1657–1659 (2001).
    [CrossRef]
  21. J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
    [CrossRef]

2010 (2)

C. R. Liao, Y. Wang, D. N. Wang, and L. Jin, “Femtosecond Laser Inscribed Long-Period Gratings in All-Solid Photonic Bandgap Fibers,” IEEE Photon. Technol. Lett. 22(6), 425–427 (2010).
[CrossRef]

M. W. Yang, D. N. Wang, Y. Wang, and C. R. Liao, “Long period fiber grating formed by periodically structured microholes in all-solid photonic bandgap fiber,” Opt. Express 18(3), 2183–2189 (2010).
[CrossRef] [PubMed]

2009 (3)

L. Wei, J. Weirich, T. T. Alkeskjold, and A. Bjarklev, “On-chip tunable long-period grating devices based on liquid crystal photonic bandgap fibers,” Opt. Lett. 34(24), 3818–3820 (2009).
[CrossRef] [PubMed]

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

Q. Shi and B. T. Kuhlmey, “Optimization of photonic bandgap fiber long period grating refractive-index sensors,” Opt. Commun. 282(24), 4723–4728 (2009).
[CrossRef]

2008 (3)

2007 (5)

2006 (3)

2002 (2)

X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
[CrossRef]

X. W. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002).
[CrossRef]

2001 (2)

1999 (1)

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

Ahn, T. J.

Alkeskjold, T. T.

Bennion, I.

X. W. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002).
[CrossRef]

X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
[CrossRef]

Bjarklev, A.

Chung, Y.

Dong, X. Y.

Eggleton, B. J.

Fang, Q.

Feinberg, J.

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

Fu, L. B.

Grubsky, V.

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

Han, W. T.

Ho, H. L.

Iredale, T. B.

T. B. Iredale, P. Steinvurzel, and B. J. Eggleton, “Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre,” Electron. Lett. 42(13), 739–740 (2006).
[CrossRef]

Jin, L.

Jin, W.

Joannopoulos, J. D.

Johnson, S. G.

Ju, J.

Kai, G. Y.

Kim, B. H.

Kim, B. Y.

Kim, D. Y.

Knight, J. C.

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

B. T. Kuhlmey, F. Luan, L. B. Fu, D. I. Yeom, B. J. Eggleton, A. M. Wang, and J. C. Knight, “Experimental reconstruction of bands in solid core photonic bandgap fibres using acoustic gratings,” Opt. Express 16(18), 13845–13856 (2008).
[CrossRef] [PubMed]

Kuhlmey, B. T.

Q. Shi and B. T. Kuhlmey, “Optimization of photonic bandgap fiber long period grating refractive-index sensors,” Opt. Commun. 282(24), 4723–4728 (2009).
[CrossRef]

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

B. T. Kuhlmey, F. Luan, L. B. Fu, D. I. Yeom, B. J. Eggleton, A. M. Wang, and J. C. Knight, “Experimental reconstruction of bands in solid core photonic bandgap fibres using acoustic gratings,” Opt. Express 16(18), 13845–13856 (2008).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. Mägi, B. T. Kuhlmey, and B. J. Eggleton, “Long period grating resonances in photonic bandgap fiber,” Opt. Express 14(7), 3007–3014 (2006).
[CrossRef] [PubMed]

Lægsgaard, J.

Lázaro, J. M.

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

Lee, B. H.

Liao, C. R.

C. R. Liao, Y. Wang, D. N. Wang, and L. Jin, “Femtosecond Laser Inscribed Long-Period Gratings in All-Solid Photonic Bandgap Fibers,” IEEE Photon. Technol. Lett. 22(6), 425–427 (2010).
[CrossRef]

M. W. Yang, D. N. Wang, Y. Wang, and C. R. Liao, “Long period fiber grating formed by periodically structured microholes in all-solid photonic bandgap fiber,” Opt. Express 18(3), 2183–2189 (2010).
[CrossRef] [PubMed]

Lim, S. D.

Liu, B.

Liu, Y.

Liu, Y. G.

Lopez-Higuera, J. M.

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

Luan, F.

Luo, J.

Mägi, E. C.

Moore, E. D.

Noordegraaf, D.

Paek, U. C.

Park, Y.

Rao, Y. J.

T. Zhu, Y. J. Rao, and J. L. Wang, “Characteristics of novel ultra-long-period fiber gratings fabricated by high-frequency CO2 laser pulses,” Opt. Commun. 277(1), 84–88 (2007).
[CrossRef]

Ren, G. B.

Rindorf, L.

Scolari, L.

Shi, Q.

Q. Shi and B. T. Kuhlmey, “Optimization of photonic bandgap fiber long period grating refractive-index sensors,” Opt. Commun. 282(24), 4723–4728 (2009).
[CrossRef]

Shu, X. W.

X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
[CrossRef]

X. W. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002).
[CrossRef]

Shum, P.

Skorucak, A.

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

Starodubov, D. S.

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

Steinvurzel, P.

Tong, W. J.

Wang, A. M.

Wang, D. N.

Wang, J. L.

T. Zhu, Y. J. Rao, and J. L. Wang, “Characteristics of novel ultra-long-period fiber gratings fabricated by high-frequency CO2 laser pulses,” Opt. Commun. 277(1), 84–88 (2007).
[CrossRef]

Wang, Y.

C. R. Liao, Y. Wang, D. N. Wang, and L. Jin, “Femtosecond Laser Inscribed Long-Period Gratings in All-Solid Photonic Bandgap Fibers,” IEEE Photon. Technol. Lett. 22(6), 425–427 (2010).
[CrossRef]

M. W. Yang, D. N. Wang, Y. Wang, and C. R. Liao, “Long period fiber grating formed by periodically structured microholes in all-solid photonic bandgap fiber,” Opt. Express 18(3), 2183–2189 (2010).
[CrossRef] [PubMed]

Wang, Y. P.

Wang, Z.

Wei, L.

Weirich, J.

Xiao, L. M.

Xuan, H. F.

Yang, M. W.

Yeom, D. I.

Yu, X.

Zhang, L.

X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
[CrossRef]

X. W. Shu, L. Zhang, and I. Bennion, “Sensitivity characteristics of long-period fiber gratings,” J. Lightwave Technol. 20(2), 255–266 (2002).
[CrossRef]

Zhang, L. R.

Zhu, T.

T. Zhu, Y. J. Rao, and J. L. Wang, “Characteristics of novel ultra-long-period fiber gratings fabricated by high-frequency CO2 laser pulses,” Opt. Commun. 277(1), 84–88 (2007).
[CrossRef]

Electron. Lett. (1)

T. B. Iredale, P. Steinvurzel, and B. J. Eggleton, “Electric-arc-induced long-period gratings in fluid-filled photonic bandgap fibre,” Electron. Lett. 42(13), 739–740 (2006).
[CrossRef]

IEEE Photon. Technol. Lett. (2)

C. R. Liao, Y. Wang, D. N. Wang, and L. Jin, “Femtosecond Laser Inscribed Long-Period Gratings in All-Solid Photonic Bandgap Fibers,” IEEE Photon. Technol. Lett. 22(6), 425–427 (2010).
[CrossRef]

V. Grubsky, A. Skorucak, D. S. Starodubov, and J. Feinberg, “Fabrication of long-period fiber gratings with no harmonics,” IEEE Photon. Technol. Lett. 11(1), 87–89 (1999).
[CrossRef]

J. Lightwave Technol. (1)

Opt. Commun. (4)

J. M. Lázaro, B. T. Kuhlmey, J. C. Knight, J. M. Lopez-Higuera, and B. J. Eggleton, “Ultrasensitive UV-tunable grating in all-solid photonic bandgap fibers,” Opt. Commun. 282(12), 2358–2361 (2009).
[CrossRef]

Q. Shi and B. T. Kuhlmey, “Optimization of photonic bandgap fiber long period grating refractive-index sensors,” Opt. Commun. 282(24), 4723–4728 (2009).
[CrossRef]

X. W. Shu, L. Zhang, and I. Bennion, “Fabrication and characterisation of ultra-long-period fibre gratings,” Opt. Commun. 203(3-6), 277–281 (2002).
[CrossRef]

T. Zhu, Y. J. Rao, and J. L. Wang, “Characteristics of novel ultra-long-period fiber gratings fabricated by high-frequency CO2 laser pulses,” Opt. Commun. 277(1), 84–88 (2007).
[CrossRef]

Opt. Express (9)

S. G. Johnson and J. D. Joannopoulos, “Block-iterative frequency-domain methods for Maxwell’s equations in a planewave basis,” Opt. Express 8(3), 173–190 (2001).
[CrossRef] [PubMed]

P. Steinvurzel, E. D. Moore, E. C. Mägi, B. T. Kuhlmey, and B. J. Eggleton, “Long period grating resonances in photonic bandgap fiber,” Opt. Express 14(7), 3007–3014 (2006).
[CrossRef] [PubMed]

D. I. Yeom, P. Steinvurzel, B. J. Eggleton, S. D. Lim, and B. Y. Kim, “Tunable acoustic gratings in solid-core photonic bandgap fiber,” Opt. Express 15(6), 3513–3518 (2007).
[CrossRef] [PubMed]

D. Noordegraaf, L. Scolari, J. Lægsgaard, L. Rindorf, and T. T. Alkeskjold, “Electrically and mechanically induced long period gratings in liquid crystal photonic bandgap fibers,” Opt. Express 15(13), 7901–7912 (2007).
[CrossRef] [PubMed]

L. Jin, Z. Wang, Q. Fang, Y. Liu, B. Liu, G. Y. Kai, and X. Y. Dong, “Spectral characteristics and bend response of Bragg gratings inscribed in all-solid bandgap fibers,” Opt. Express 15(23), 15555–15565 (2007).
[CrossRef] [PubMed]

Y. P. Wang, W. Jin, J. Ju, H. F. Xuan, H. L. Ho, L. M. Xiao, and D. N. Wang, “Long period gratings in air-core photonic bandgap fibers,” Opt. Express 16(4), 2784–2790 (2008).
[CrossRef] [PubMed]

B. T. Kuhlmey, F. Luan, L. B. Fu, D. I. Yeom, B. J. Eggleton, A. M. Wang, and J. C. Knight, “Experimental reconstruction of bands in solid core photonic bandgap fibres using acoustic gratings,” Opt. Express 16(18), 13845–13856 (2008).
[CrossRef] [PubMed]

L. Jin, Z. Wang, Y. G. Liu, G. Y. Kai, and X. Y. Dong, “Ultraviolet-inscribed long period gratings in all-solid photonic bandgap fibers,” Opt. Express 16(25), 21119–21131 (2008).
[CrossRef] [PubMed]

M. W. Yang, D. N. Wang, Y. Wang, and C. R. Liao, “Long period fiber grating formed by periodically structured microholes in all-solid photonic bandgap fiber,” Opt. Express 18(3), 2183–2189 (2010).
[CrossRef] [PubMed]

Opt. Lett. (4)

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Figures (6)

Fig. 1
Fig. 1

(a) (Color online) The bandgaps, fundamental core mode of the all-solid fiber, spectra before and after inscription of the 240 μm period of LPFG. The inset is the cross section of the all-solid fiber. The red curve represents the dispersion curve of the fundamental core mode. The orange and purple curves represent spectra before and after inscription respectively. (b) The periodic notches on the all-solid fiber after inscription. (c) The cross section of the all-solid fiber at a notched region corresponding to the left end of the fiber shown in Fig. 1(b).

Fig. 2
Fig. 2

(Color online)The normalized spectra for different periods of LPFGs. The black solid curves and red dash curves represent spectra of the LPFGs before and after being immersed into a high index liquid respectively. The insets are near field images corresponding to these resonance peaks.

Fig. 3
Fig. 3

(Color online) The period of a grating and dispersion factor against the resonance wavelength. The red curves represent the phase-matching condition of an LPFG, the black horizontal lines represent the periods of LPFGs, the blue curve represents the relation between dispersion factor and the resonance wavelength.

Fig. 4
Fig. 4

The schematic diagram in the cutback experiment.

Fig. 5
Fig. 5

The evolution of light field for a 240 μm period of grating. (a)-(j) present the experimental results, (k)-(p) present the simulation results. The observation wavelength and the distance between the observation point and the input end of the LPFG are given in each figure.

Fig. 6
Fig. 6

The evolution of light field for a 260 μm period of grating inscribed in another PBGF whose pitch is about 9,5 μm. (a)-(e) present the experimental results, (f)-(j) present the simulation results. The observation wavelength and the distance between the observation point and the input end of the LPFG are given in each figure.

Tables (1)

Tables Icon

Table 1 The resonance order, resonance wavelength and temperature sensitivity corresponding to each resonance peak

Equations (8)

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d λ res d T = λ res γ ( α + ξ s n e f f , s ξ c n e f f , c Δ n e )
d u d z = i M c κ u + i M c g κ g , q exp ( i 2 δ z ) u
κ = c 1 κ
κ m n = ω A e m * Δ ε e n d A
c m n = A ( e m * × h n + e n × h m * ) z d A
κ g , q = c g 1 κ g , q
κ g , q , m n = 2 ω Λ Λ 2 Λ 2 A e m * Δ ε g ( z ) e n exp ( i q G z ) d A d z
2 δ m n = β n ( β m + q G )

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